Proposed resolution:

This wording is relative to N4981.

1. Modify [alg.fold] as indicated:

   template<input_iterator I, sentinel_for<I> S
            indirectly-binary-left-foldable<iter_value_t<I>, I> F>
     requires constructible_from<iter_value_t<I>, iter_reference_t<I>>
     constexpr see below ranges::fold_left_first_with_iter(I first, S last, F f);
   template<input_range R, indirectly-binary-left-foldable<range_value_t<R>, iterator_t<R>> F>
     requires constructible_from<range_value_t<R>, range_reference_t<R>>
     constexpr see below ranges::fold_left_first_with_iter(R&& r, F f);
   

   -9- Let U be

   decltype(ranges::fold_left(std::move(first), last, iter_value_t<I>(*first), f))
   

   -10- Effects: Equivalent to:

   if (first == last)
     return {std::move(first), optional<U>()};
   optional<U> init(in_place, iter_value_t<I>(*first));
   for (++first; first != last; ++first)
     *init = invoke(f, std::move(*init), *first);
   return {std::move(first), std::move(init)};
   

   -11- Remarks: The return type is fold_left_first_with_iter_result<I, optional<U>> for the first overload and fold_left_first_with_iter_result<borrowed_iterator_t<R>, optional<U>> for the second overload.

ranges::fold_left_first_with_iter constructs the initial value through optional<U>(in_place, *first) which is not quite right, because the exposure constraint only ensures that U can be constructed from the value type of the iterator rather than its reference (demo):

#include <ranges>
#include <algorithm>

struct Op {
  Op() = default;
  Op(std::tuple<int>);
  Op(std::tuple<int&>) = delete;
  Op operator()(Op, std::tuple<int&>) const;
};

int main() {
  std::ranges::fold_left_first_with_iter(
    std::views::zip(std::views::single(0)), 
    Op{}
  ); // hard error in libstdc++ and MSVC-STL
}