Assuming the single template argument version. If T has an implicit constructor taking type R as argument, wouldn't the second argument into max of type R be implicitly converted to T before getting passed to the max function? So there is no need for a special version taking both L and R?

This is a property of c++ implicit constructor rules, it is not unique to this function. In most cases this is something you want to avoid but for integer promotion it can some times be useful.

Nope, template type deduction never implicitly converts: https://godbolt.org/g/stZBK1

Oh, "conflicting types for parameter 'T' ('T2' vs. 'T1')". I'm surprised but it's a nice surprise. Finally something in c++ where safety is valued more than implicit dangerous magic.

C++'s type system has always been stricter than C's. Even the following, totally valid C program, is ill-formed C++

    int* x = malloc(5 * sizeof (int));

because in C++ you cannot implicitly cast a void pointer.