I've always viewed essence in this game as the breath of life. To me, it was like your Sovereign was taking part of his/herself, directing it into the world, and using this purest form of magic to revive the shattered lands. To totally take that away from building the first city seems weird to me. I think that the first city should claim essence, and all others claim materials - this first city is meant to be your shining beacon on the world. It should be a personal investment, I feel. The others are just the result of expansion.
I also really like the idea of your Sovereign spending essence for the sake of ultimate structures and city empowerment abilities. Going from Demiansky's examples...
Altar of Elements: Use 5 essence and commit your Sovereign for 10 turns. This structure offers +15% to essence creation, .05 essence/turn for each node you control, and units produced by the city where the Altar is build have a 30% chance of gaining a free, permanent and basic enchantment of one of the four elements.
The forces of the elements seem somewhat primal in comparison to the technology of cities and the paths of life and death. However, by commiting part of your very being to the elemental powers that surround your city and gently guiding some of those powers towards this focal point, you can slowly recharge your essence and every unit produced may have the fortune of elemental energies lingering around them.
Lore Spire: Use 5 essence and commit your Sovereign for 10 turns. This structure offers nothing initially, but for every battle your faction wins, it offers +1 to the happiness of this city and +.5 to the happiness of all other cities.
This stone just appeared one day by your command, initially just that - a stone. Yet each battle won earns this stone lines of runes that glow with faint magic. These runes glow faintly, detailing victories that seem far away yet are still infinitely important to the people. As the edifice grows in its glowing runes, so too does the faith your people hold on you, for how can they deny this structure, bound to your very being and speaking of each victory under your lordship?