I think if that works it would be a great solution! Processing copyright claims is pretty time-consuming, so they‘d have to put a lot of work into it

But the Reddit ToS states that by submitting content to their Services you

grant [Reddit] a worldwide, royalty-free, perpetual, irrevocable, non-exclusive, transferable, and sublicensable license to use, copy, modify, adapt, prepare derivative works of, distribute, store, perform, and display Your Content