A lot of the issue with the teams sitting deep after you've had some success comes from most of the PL teams (if not all, I haven't looked) has DEEP DEFENSIVE LINE as one of their advanced tactics and as soon as you appear a threat, lots of teams use their most defensive tactics (sometimes combined with a def mentality) against you from the off. A bit more tactical variety among the teams would decrease this boredom.
I've only just got into the Europa League (starting 4th season soon with Reading ML defaults) so it will be interesting to see if I find any super powered teams there. But in my FA Cup matches last season (I got to the semis) the weak teams I played certainly weren't boosted at all. Only in one game had it felt a little handicapped for me and that was in the second match in the cup. In this match I needed to rest a lot of players and so my team mentality went from it's usual high 80s/early 90s to about 65-70, so I was expecting my players to have a few issues anyway.
Fingers crossed I don't suffer the same issues as him as I'm now also starting my 4th season playing on TP...