On further thought, it seems like your function is exactly equivalent to:
> static_cast<T>(x) == x

Can you really argue that this expression is sufficiently common and
sufficiently annoying to warrant a new function in the standard
library? What I'm getting at is that you need rationale for all the
specifics, and whether each of these functions has a right to exist.
At the very least, you could use this as a *Returns* paragraph, if it
is exactly equivalent.

Similarly, you make a claim about "extremely inefficient" codegen in
your motivation, but you don't provide a concrete example. Extreme
claims need some evidence.