Why does the performance of this non-matching pattern scale with the size of the search space?

It's simply because libstdc++ and libc++ do not implement such optimization.

The following is the main part of libstdc++'s implementation of regex_search:

template<typename _BiIter, typename _Alloc, typename _TraitsT,
     bool __dfs_mode>
  bool _Executor<_BiIter, _Alloc, _TraitsT, __dfs_mode>::
  _M_search()
  {
    if (_M_search_from_first())
      return true;
    if (_M_flags & regex_constants::match_continuous)
      return false;
    _M_flags |= regex_constants::match_prev_avail;
    while (_M_begin != _M_end)
    {
      ++_M_begin;
      if (_M_search_from_first())
        return true;
    }
    return false;
  }

So it does traverse the whole range even if the regular expression contains ^.

So is libc++'s implementation.