For people that are afraid of running out of essence - don't run out! For every chicken little "what if" I haven't seen how a slow regen of essence helps, and often what is suggested trivializes it.
I picture essence as your innermost self, and sometimes there just isn't enough of "you" to go around.
And pray tell, why does your 'innermost self' have to be hard-capped? Don't go citing some debatable philosophical/metaphysical notion as a good reason for a major gameplay feature. Those things should be invented afterwards to give depth to the game world for features that are implemented for the sake of gameplay - not the other way around.
And can you predict how long a given game will be? Hard-caps are not flexible, they work (sometimes) as long as you stay within their intended limits, and result in unadulterated annoyance and frustration when you exceed them. If you play a game that is longer or more chaotic than this hard-cap is intended for, essence will become trivial because no one will have any and it may as well not be there. It'll serve a purpose in the beginning of such games, but then as channelers run out (as they inevitably will) it will become a non-factor. Not fun...
On the other hand, if there are ways of getting more essence then those games can continue as they should and essence will remain important.
Limited essence makes essence more valuable and the decisions of when to spend it critical. If you are worries about running out, then I have no problem with being able to "level up" your channeler to get more essence. But I would hate for it to recharge your "essence battery" rather you could access inner reserves that you didn't know you had. It may seem a slim distinction, but it is a significant one. The "trickle/recharge" means that you can just hole up and hide and wait for a recharge - again this trivializes it imho. And leveling up I think should follow the levelling curve of D&D or popular MMOs - the first levels should come pretty easy and fast, later levels should require some pretty major accomplishments to gain (I don't even know if they are doing levels, lol). I also don;t think that there should ever be a level cap. That way no matter how long a game went, there would always be the ability to gain level and access more essence.
I agree with you completely about the distinction between recharging your batteries vs. accessing/gaining more. Nonetheless a very small but constant trickle (which maybe should be uniform for all channelers - no way to modify it) could still work well, I think. Yeah it means you could sit in a hole until your channeler is competitive again if something goes horribly wrong - and if the other players let you then why not? If you are in such a vulnerable position and yet manage to fend off aggressors or stay out of conflicts, then you deserve a second chance. And a trickle of essence could correspond to 'inner reserves that you didn't know you had', or even to simply becoming a more powerful channeler through age, experience, time, whatever. Other methods of gaining new essence that I think have potential (and have been suggested before) are as quest rewards and by draining it from other essence-wielding beings.
And I'm not sure how I feel about the whole level thing. I'd almost rather levels affect other channeler stats, and then have those stats modified by essence. A channeler stats could be multiplied by how much essence they hold. This way a very experienced channeler with little hoarded essence might be able to stand toe-to-toe with an unexperienced channeler with quite a bit of it. This could make for some interesting strategies, I think - and different viable options.
It seems like the people overly concerned about running out of essence want to have their cake and eat it to. Sometimes, making serious choices and dealing with the permanent consequences actually increases the fun and makes you feel like you are doing something major - using essence I think should have that feel of "This is one of the BIG STRATEGIC decisions". Recharging and recouping are two ways that I feel really diminish essence. I agree, having ways to get more is important for long (never-ending?) games. I know one thing I want to do is sandbox my empire long term, and it would suck to do that with no essence EVER.
Personally, I want permanent consequences. If I invest a huge amount of essence into making a super champion and then send him to his death, I want to feel it. I want to be able to get more essence over time, but no matter what I will always be set back by all that essence I lost on that champion. With that same investment other channelers could have made much better use of their essence than mine. You'll still have permanent consequences as long as you can't get essence even remotely as quickly as you can use it. If you can't get more essence then you can't recover from major setbacks. If you can, then you still have a chance to recover but you will always feel the effects in the form of lost opportunity (which is significant).
There really isn’t an easy way to figure or even argue how essence should work since we don’t know “exactly” how it is meant to function in the game. I do agree that essence should not be trivialized but I also think if Elemental did implement some kind of limited and slow regeneration of essence it wouldn’t cause it to be irrelevant. The key balance as I see it in this discussion is making essence vital and strategic without it becoming a quagmire that ruins the fun factor of long games.
I think you just summed up this whole thread 
I’m leaning towards regeneration because it wouldn’t have to be 100% regeneration but just enough to perform basic essence related action. That way even in the longest of games you could still be a semi-functional Channeler restoring land, imbuing champions / artifacts, casting essence spells just with diminished capabilities. It would still be very important for you to manage your essence properly but you wouldn’t totally be screwed over. One could argue in such a situation where the Channeler was essentially functioning on emergency power only the strategic value of essence would increase by an order of magnitude.
I largely agree with you but I don't want the channelers of the world to all be running on emergency power every time the game goes on for a long time. It's anticlimactic. I'd much rather give channelers the opportunity to bide their time and build up their essence stores again (or use it as they get it - each could have its advantages). But again, getting more essence should take a very long time, such that you can always use essence much faster than you can get it.
I’ve also been trying to refine something GW said a while ago about “0 essence = death”. If Elemental did have a 100% finite essence system where after you obtain your max essence you never get any more you could still give the player the option to use essence abilities but with a cost associated with them. In another post I said something like
Red abilities: Have 20% below the required essence for an action, high risk of death or power loss.
Yellow abilities: Have 10% below the required essence for an action, low risk of death or power loss
Blue abilities: Have the required essence for an action, no risk of death or power loss.
If you expanded this a bit more and give the player someway to reduce the % chance of death I would find a 100% finite essence system very interesting late game. Concerns about no essence late game would be addressed yet the strategic value of essence overall would increase. Every Channeler would be trying to avoid desperate situations where casting that essence spell that could save your nation might also end up killing you. This would also reward people who effectively managed their essence. This is all just speculation though but I think it sounds interesting.
I don't like that at all. For one, channeler death apparently means endgame (which I personally love). That said, turning your channeler's life into a game of luck does not appeal to me one bit. At that point it's gambling, not strategy. It'd actually not be quite as terrible, in my opinion, as long as the chance of death is high (but I'd still be very unhappy with this). The reason is, if I get my chance of death down to, say, 3% and then cast my spell and die, I will be angry and frustrated.