Pot 1
Real, Atletico, City, Bayern, Juventus, Benfica, PSG, Shaktar
Pot 2
CSKA Moscow, Ajax, Galatasaray, Anderlecht, Olympiakos, Basel, APOEL, Nicosia, Aalborg
Pot 3
Salzburg, Sparta Praha, Steaua Bucuresti, Maccabi Tel-Aviv, BATE Borisov, Legia Warzawa, Dinamo Zagreb, Malmø
Pot 4
Celtic, Partizan Belgrade, Slovan Bratislava, Molde, Ludogorets, Debrecen, Maribor, Dinamo Tbilisi
You're only missing Barca really. Nobody cares about Chelsea. Could always skip the last pot in favour of cup winners (or league runners up).
Barca, Arsenal, Dortmund, Napoli, Porto, Guingamp, Dynamo Kiev, FK Rostov
Would this make for a much worse competition? In the group stage, not at all. Knock rounds would be pretty much the same from the QFs.
Might even force clubs to spend less on wages and invest their money properly as they won't be in the competition every season (Bayern, Barca, Real, Porto and Juventus excluded).