I feel the same about Hameed at the moment tbh, he’s only done it over 3 matches on Indian pitches, but he can only perform on what he’s given, and he should definitely be in there for the start of the summer’s tests, injuries allowing. Jennings, let’s wait and see, but getting another top 4 batsman has been a pain in the arse for ages now.
I think Jimmy is on the way out, I’d probably play him in 2/4 or 3/5 tests, save him for the best conditions for him. Too slow if there’s no help from the pitch. Plus Wood is maybe the reverse, but fragile, so play him in the games that Anderson doesn’t.
Ali definitely has to play at the moment, offers too much with bat and ball to overlook him, and he’s probably enough spinner for most english grounds (maybe stick in rashid as well for oval and old trafford).
Buttler is doing enough to be picked on batting alone. I’d be very tempted to give him the gloves and have Bairstow as a pure batsman at 5.
Cook*, Hameed, Jennings, Root, Bairstow, Stokes, Ali, Buttler+, Woakes/Rashid/Ball/Finn, Broad, Anderson/Wood. Gives you 2 pacemen, Ali with spin, Stokes as an all rounder, plus one more proper bowler, but also gives you 8 proper batsmen (plus Woakes if you go that way).