To answer the title question: Yes, heroes - and namely Commanders - absolutely, positively should gain XP from managing a city and it's a huge oversight they don't. On that topic, the 0.25 XP/turn from the Adventurers Guild's bonus to stationed heroes is completely ridiculous - 0.25 is such a tiny amount it is utterly meaningless. I don't know what the developers were thinking there, the amount gained should be ten times as much or higher to begin to become even remotely meaningful.

So no, you're not doing anything wrong, this is just another of those 'wtf were they thinking' things... You are entirely correct that there is currently no good way to level an administration-focused hero.

I thought I replied to this already... anyways, if you want your units to gain more xp in the city, I made a mod specifically for this purpose... which gives Monuments, Guardian Statues and Guardian Idols (same upgrade path) bonuses to experience.  It gives an XP amount to stationed units each turn, and a slightly larger amount to stationed champions.  This does change your 'approach' to the game a bit, and I obviously like it personally, but of course YMMV.  More details here:

Monuments XP v1 mod

In case that interests you.

Back on topic, the 25% thing is a red herring.  The Adventurer's Guild, as well as the Arena, War College and War Temple always give 1 XP each turn.  Adventurer's guild only gives the XP to Champions or Sovereigns, though.  So your champions will gain 1 XP per turn if you have the Adventurer's guild in that city, 2 XP if you have the Arena as well, and 3 XP if the War College/War Temple are also present.  Units will gain 2 XP/turn if both the Arena and War College/Temple are in the same city.

Some people think XP should mainly only come from killing things and questing, though, hence the current state of the game.  I'm obviously not in that particular camp, but the powers that be (Stardock) make the final 'official' decision on this.  If a LOT of people demand a change though, maaaaaybe we'll get one, but in the meantime, if you want to try another approach(es), your trusty modding community is here to help!

tjashen is correct, it's been reported and hasn't been fixed. I for one don't think they need to fix the 25% chance to get XP, but an increase to the XP would be better in general. If they were to fix the 25% then they should up the XP given to around 5.

If it were 25% chance of getting 5 xp while sitting in a city, would not defeat their intended purpose of forcing you to do hero things. Currently doing hero things become managing the lairs to get a good amount of XP, I find it is better not to remove a large number of lairs around my cities, instead I harvest them for XP, and this has worked quite nicely. Should it not be that one should clear these lairs from the creatures within to protect your borders. But one leaves them sitting there which doesn't seem like a good story. It is different when not clearing difficult lairs near your cities, but in general it should be cleared when possible otherwise it seems rather meta gaming to remove these lairs.

I would find it far more entertaining if the adventurers guild spawns new lairs with a  25% chance within 10 radius from the city as adventures tell of their stories and discuss found ruins with creepy things in them.