Of course we had success with Premier League players. We signed a shitload of players from other English clubs over the years. Who was the last absolutely unqualified success signed from another Premier League club? Van Persie, I guess. Ten years ago.
I think we signed a grand total of... five players from the Bundesliga. Of those, one was destroyed by injuries and one was simply past it - neither of those things has anything to do with the league they had previously played in.
The other three were Kagawa, Mkhitaryan, and Sancho. So perhaps we should just avoid signing slight technical attacking midfielders from Borussia Dortmund. And even for that conclusion the sample size is probably not enough.