It's curious the hate Utd and Liv have for each other. For me, not living in England, it's a learned hate without the venom.
But, I love the PL, and I've always fought the urge to actually support 'Pool during CL. I believe a strong PL means the chances are better top players will want to play for us, so I instinctively want to support Liverpool. Plus, my best mate is a Liverpool fan.
I'm all for football tribalism, but it's actually quite funny how I must consistently stop myself from being happy when Liverpool scores against a European side.
Anyway
Unless you never tune in for UK based English commentary, pre match, post match and PL, CL related stuff, it would always appear weird to everyone else, who actually "get it".
How biased Liverpool love in media can be is blatantly disgusting. It's disguised under the PL vs the rest. Yet there has been an ABU culture too, that rubbed it in every chance they can, even it's Man Utd on the receiving end of the big bad European bully.
I meant supporting a club doesn't mean support a league. That's what Liverpool supporters had been for decades where they had conspiracy theory about the creation of PL. Which we happened to dominate during SAF reign. Even with recent success, deep down they would prefer their pre PL dominance because they were also force in European competition pre PL. Didn't it happen to you how often they flash the 5 fingers thing (before winning thier recent 6th)?
Similarly, Real Madrid, Barcelona, Milan, Juventus... when they dominated not only the league but also Europe, didn't care much about the league. The top players flocked there, and still are because the prestige and money (they didn't always acquire revenue cleanly either). The issue here is new money is too much and PL strong media coverage and policy is easier for new money to pour in. In no way those teams want their league to be strong. They sugarcoat their ambition to keep their status quo because they know with new money going this way, it's more difficult for them to compete (not that they can't compete).
PL become stronger doesn't always necessarily mean the top players would be more likely to come play for us. Some players would always have the preference for Real Madrid, Barcelona, Bayern, Milan... if those clubs can pay the same. Many players would be ready to come to Chelsea, Newcastle, City for the money too. PL may become an absolute super league, doesn't make us more prestigious without those silverware. Serie A is an example. There were competitive teams than just Milan and Juventus, but when it's boiled down, only teams that won a lot get the spot light in history book and being more relevant in the future.
In short, in your own league, your focus is your own success. Your rival success is never good for you.