Although i can see Pool doing better in the EPL, i see two reasons that it wouldnt matter.
I am not sure about the new owners willing to spent as much as Manure and Chel$ki, but it is really hard, nearly impossible, to build a team, with the same depth and world class % of players, if you dont invest more or the same.
Pool's type of players favors cap type of competitions and they naturally turned their attention/focus there. You have to be pleased by the performances, Pool had, in the CL.
The increase of investment is not Rafa's choice and a new coach woulsnt change that.
Rafa can as well make a team to challenge for the championship, but he feels he has less chances there and you would disappoint you, if the team was worthless in Europe, there lies Pools power, the fans, the glory, the sponsors are all fed by those success, should he risk to lose them for a faint hope of a domestic title?
And what makes you think that you can find a coach as good as him?
Even nearly as good as him?