I agree with you about taking a long term approach, and think he sounds like a pretty good player to target, but I disagree with much of your post apart from that.
Liverpool haven't targeted championship players much at all as far as I can tell. Most of Klopp's early signings were players with experience in the premier league or another top league who were near their mid-twenties, but were not attracting enough hype or attention to require huge fees. Mane, Wijnaldum, Matip, and the like were ready to step in and help the club reach top 4 quickly, even if they obviously weren't good enough to win major trophies. As the team improved and qualified for champions league, they attracted bigger names and spent more money. Recently, they've focused a lot on young talents like Elliott and Hoever, but haven't spent a fortune on them.
A player like Bellingham could really help United in 3-4 years, but they need someone to bridge the gap, and help make progress toward their goals. If they aren't winning more, they wont have a strong locker room culture for players like him to mature and develop. I think the issue is worsened by United's seemingly limited ability to focus on multiple targets at once. If they can only sign 3 players in a summer window, and maybe 1 in the winter, they need to go for ones who can help now, but who are young enough to help in 4-5 years as well.
