[re.alg.replace] says:

template <class traits, class charT, class ST, class SA>
basic_string<charT, ST, SA>
regex_replace(const basic_string<charT, ST, SA>& s,
const basic_regex<charT, traits>& e,
const charT* fmt,
regex_constants::match_flag_type flags =
regex_constants::match_default);

This doesn't compile, though:

#include <string>
#include <regex>

int main()
{
  std::regex_replace<std::regex_traits<char>, char>(std::string("x"), std::regex("x"), "y");  // works

  std::regex_replace(std::string("x"), std::regex("x"), "y");  // fails

  return 0;
}

The string,regex,string,flags overload doesn't work because the arguments aren't an exact match.