A question about the argument types to the comp predicate in std::lower_bound

Reference: std::lower_bound

Excerpt:

comp    -   binary predicate which returns ​true if the first argument is less than (i.e. is ordered before) the second.

The signature of the predicate function should be equivalent to the following:

 bool pred(const Type1 &a, const Type2 &b);

While the signature does not need to have const &, the function must not modify the objects passed to it and must be able to accept all values of type (possibly const) Type1 and Type2 regardless of value category (thus, Type1 & is not allowed, nor is Type1 unless for Type1 a move is equivalent to a copy (since C++11)).

What I would like to clarify in the above excerpt with respect to the type mandate is the following:

nor is Type1 unless for Type1 a move is equivalent to a copy (since C++11)

I presume Type1& is not allowed as that could potentially allow the predicate to modify the objects passed in; but why is Type1 not allowed? Is it only due to optimization, taking cues from the precondition that Type1 is allowed if a move is equivalent to copy? Or is there more to it than that?

TIA