Is it just state? Maybe. Or maybe it's a glorified calculator. Or maybe it's both.

You don't actually lose anything. Lambda calculus and Turing machines are provably equivalent, so it may be more accurate to regard them as two aspects of the same thing. As such, pick that which is best suited to what you're attempting to do, otherwise there will be more pain than necessary.

I learned this the hard way when working on some projects with prolog. While prolog is not functional (and I really don't like the language either), it's proof enough to me that there are some problems I'd rather not do in imperative.

However, you may point out the things I was working on were fairly esoteric, and you'd be right...