Why must these be enum classes instead of simple bools?

It is fun to read nothrow NoThrow = nothrow::no (no, NoThrow!) but noexcept(IsNoThrow) might be clearer...

Pre-existing

Because it is much more difficult to reason about what meow<true> does compared to meow<nothrow::no>

Also it is much harder to accidentally pass the wrong thing

Especially in this case where it is

trace_iterator<Cat, true, false, true>

Are you sure those are in the right order?

nothrow is a terrible name. How many times have I told someone not to put a negative in a name?

But you told them not to do it.

Nobody said you could not commit horrible code crimes

May I suggest something giving the best of both worlds (in the future, this is pre-existing, also using enum helps a ton):

enum : bool { Throws, NoThrow };
template<bool IsNoThrow = false>
struct meow { ... };

meow<NoThrow> ....

I suppose you could name the enum if you really want to, but that isn't relevant for clarity, just for preventing type confusion, but type confusion is arguably not a big deal here since really the type is bool for all of them.