I'm sorry but I honestly don't see where mines not being depleted affects versatility.
Limited resources in a game like Age of Empires means turtling more often than not results in an unwinnable, unlosable stalemate. In a TBS game with multiple victory conditions it means that those conditions that don't rely as heavily on limited resources are inherently better for longer games. With finite resources, a very evenly matched game is bound to degenerate into crap, unless you stop requiring those resources, which seems unlikely. Limited resources makes 'quick' strategies advantageous, because there is little risk of running out of resources while it's being implemented.
Maybe for when the mines are depleted, you are already doing Populus like magics and breaking havoc in the world anyways. Or you reach a quest victory. Etc. If my channeler can run out of essence and not being able to cast some spells anymore (I'm speculating here right now), why not mines? (or farms) If player cannot adapt to a situation or being able to prevent it even when he has the ability to do so, it's not the game's fault. That obviously supposes that the game offers you alternatives to military.
"Maybe" is the operative word. When resources run out will happen at totally different stages of the game every time. Sometimes it the game might be won well before it becomes an issue. Sometimes resources might run out long before anything is remotely close to being resolved. Like I said before, maybe in the essence thread, hard-capped limits on any sort of resource only ever work within some intended framework. In the case of limited resources, there is some assumption about how long a game should take and at what rate resources will be used. If those assumptions turn out to be wrong in a given game, it doesn't work. When an entire map runs out of resources and no one is in a position to win, the game is broken. That just isn't fun.
And the argument, "if essence is going to be finite, why not mines or farms?" is horrible. For one, everyone who wants essence to be limited to some predetermined number wants it to be so to differentiate essence from everything else, to make it that much more precious. And using that argument on me is even worse considering I want there to be ways to get more essence. I don't want the game to ever reach the point where my channeler becomes unable to cast spells or do anything useful (like you, this is just speculation, we don't really know how essence will affect channelers).
The onyl two real problems (players not liking it appart) that I can see are:
Really big maps. Never play those so my mind can not actually process that. No idea so...
Forcing players to play certain way. Min/maxers wil do it anyways. Find the best combo and exploit it. Those who prefer to play more casual, wouldn't enjoy being forced to play certain way because it's the onyl one to win. But I don't think that the depletion of mines would force players to be blitzers but to me more active in whatever they want to achieve. But without a system to test it (if I'm able to mod it for my games...) it's difficult to say more than it's just my opinion about it expecting to change in the evidence of being wrong.
I think limited resources really would force people to play a certain way, unless they want to risk spending hours playing a game just to discover that it will never be resolved - or at best that it'll just become a long, drawn out battle of attrition.