EDIT 3: Looking at Lua's overall implementation, it seems to be focused on being fast and lightweight.
I don't know why Lua implemented TCO, but if I had to guess, it's not because it enables you to replace loops with recursion, it's because it... optimizes tail calls. It causes tail calls to use less memory, and this is particularly effective in Lua's implementation because it reuses the stack memory that was just used by the parent call, meaning it uses memory which is already in the processor's cache.
The thing is, a loop is still going to be slightly faster than TCOed recursion, because you don't need to move the arguments to the tail call function into the previous stack frame. In a loop your counters and whatnot are just always using the same memory location, no copying needed.
Where TCO really shines is in all the tail calls that aren't replacements for loops: an optimized tail call is faster than a non-optimized tail call. And in real world applications, a lot of your calls are tail calls!
I don't necessarily love the feature, for the reasons that I detailed in the previous post. But it's not a terrible problem, and I think it at makes sense as an optimization within the context of Lua's design goals of being lightweight and fast.