Indeed.
Walcott never had great technical skill. His game was always about raw pace, and once he lost that he floundered.
Romeu spent a few years playing less intense football in Spain and looked hopelessly out of his depth against the pace and power of top Championship teams.
Lallana - well, he was just crocked so we'll never really know how much he could have contributed in that one season.
Assuming JWP has kept his fitness levels up and still has the same stamina then I think he could still be a great option. He's probably never going to get another PL contract after the the last 3 years being barely played even when fit. So I reckon it should work well for both parties.