I think Frankie will be a very good, perhaps even great, striker, but firstly I'm not sure whether that'll be with us (the current Klopp setup isn't exactly tailor made for a striker), & secondly I'm not sure how long it'll take him to get there.
I'd like to see him loaned out next season & get serious game time under his belt.
He came here specifically because he didn't want to be sucked into that black hole at Chelski where young players are simply passed from one club to another until both parties lose patience, and because he didn't want any more loan-outs himself, wanted to go somewhere he could put down roots, and was convinced he'd be brought on carefully by the coaches and given chances in the first team. So while I see the logic in your suggestion, I think it's unlikely, given his own outlook. I agree though about the need for actual game time - at the very least he needs to play for the reserves whenever possible and accumulate some goals. Ings has shown him there's no shame in that.