Another thought I just had: Those "big clubs", they are big because they‘re mostly know for, well, winning.
Like, you can lose in the quarter finals of the Champions League year in, year out and be fine because you‘re still mostly winning – both in your domestic league and the early stages of European competition. Sure, there are some dry spells and you won‘t win the domestic league every year, but you‘re still making the Top 4, which means a casual (overseas) fan can tune into one of your games and see you winning them ~80% of the time. Now, if you start focusing on playing only good teams in an ESL, you‘re bound to lose more often. Way more often. Doesn‘t that devalue your brand – and in the end the whole product? That can‘t be good for business.