This signing doesn't make any sense to me unless the plan is to move Bruno Fernandes on.
Bellingham isn't best suited to playing a deeper role in midfield imo. The game against USA exposed his lack of ability in that role where some would argue that a player like Yanus Musa was better. So in the next game, Southgate dropped Mason Mount for Henderson, which gave Bellingham more freedom as the most advanced player in a midfield 3, with Rice and Henderson occupying the two deeper roles in midfield.
We should also bear in mind that when comparing Bellingham to the likes of Keane and Vieira, is that they played football in a different era. The Premier League right now has adopted a concept of defending methodically from the front, which wasn't the case in the time of Vieira and Keane. And it wasn't until the arrival of coaches like Brendan Rodgers and Pochettino, that the change in approach was becoming more obvious and would later become widespread with the influx of numerous other coaches in the top flight.
So what we need is a deep roaming playmaker imo, to occupy a deeper role next to the more positionally disciplined Casemiro. And that deep roaming playmaker will be the one who will be expected to provide the craft and guile in midfield, which will help us effectively build play from the defensive to the middle thirds, and also thwart the opponents methodical pressing game by evading/resisting pressure in confined spaces. Bellingham isn't that player but the Argentine lad at Benfica (Enzo Fernandez) might be.
Bellingham would suit Klopp's direct approach and I can see why he'd want Bellingham. But I think for us it would cause a unnecessary headache for a ridiculous amount of money unless the plan was to sell Bruno Fernandes.
