I fundamentally disagree with your first paragraph and few other things I've highlighted. I'm not saying I think you're an idiot, just that we have opposing views on this. We do not need more matches between the best teams.(this will be a long and rambling post apologies).
The reason I believe that is because the scarcity of these matches is what makes football enjoyable. The fact that the matches between the best teams occur at the pinnacle of the game (CL quarter/semi/finals) make watching the other games worth it. If Bayern and PSG play each other more regularly then winning those games for Bayern fans becomes less valuable, losing those games for PSG becomes less crushing and whatever result for the neutral becomes less compelling. Why tune in and watch Bayern/PSG this week if you can tune in next week and the week after and watch the same thing?
Similarly, having a certain level of disparity between teams in a league or cup competition creates excitement. Variables create excitement. If peak level Barca 2009 played peak level Sacchi Milan every week then it would become a neverending slog fest.
Bielsa's Leeds United are a fantastic example of my point. Leeds are widely regarded as one of the most compelling teams to watch in world football at the moment. Not because they have unlimited funds. Not because they are hugely successful. Not because they have the greatest players. Not because they have the biggest fan base. Not because they have the most money. Not because they have the richest history. It is because they play compelling football.
I also despise the term "dead rubbers". Yes, some games mean more than others. Yes, some teams are more interesting to watch than others. That doesn't mean that less interesting games shouldn't be played though. Just because I, and the majority, would rather watch a super tense final CL group game between United and Leipzig than Ferencvaros v Dynamo Kyiv that doesn't mean that the latter game has no value. The fact that Ferencvaros could qualify at the start of the group means that final game which "means nothing" between them is necessary. Also, that game almost certainly does hold value to Ferencvaros fans who have waited years for their club to play in this competition.
The view that people are not interested in smaller teams is also nonsense. I am a united fan and have been all my life, regardless of that Leicester City winning the league is one of my fondest memories. I am sure that for people who love French football Montpellier winning the league was also a fantastic moment in sport. Likewise, Stuttgart in Germany. Greece at the Euros in 2004, Denmark...
Yes of course more people are interested in watching the latter stages of the CL than the group stages, but that is what a competition/tournament is. Just because some teams don't win as much as others doesn't mean that they aren't interesting in a sporting sense. Agnelli going after Atalanta is full on insanity. Atalanta earned their right to play at the top table by playing great football. I would rather watch Atalanta play week in week out than Juve. Likewise, as a neutral, Leeds are more interesting to watch than United. I obviously watch United because I care deeply whether they win or lose.
My opinion is fundamentally that I want variety in the football I watch. I want to play Burnley on a Sunday and have a physical and tactically tight game and then play Roma on a Thursday and have an open and attacking game. Both have value and I want to watch both pretty much equally.
I don't think our views are that far apart. You can hold both the opinions that "fundamentally that I want variety in the football I watch", but also believe that "the best teams should compete against each other with greater regularity", and not be contradicting yourself.
The last two European champions are Liverpool and Bayern Munich. They've played two competitive matches of football against each other in the last 20 years; just three matches in the last 40 years! The two best sides in the world currently are probably City and Bayern. They haven't played for six seasons! So many great sides of recent times are just passing each other like ships in the night. Barcelona and Bayern have played two matches in six seasons! The current Champions League is engineered to protect the largest clubs in a commercial sense, by keeping them apart as much as possible until the last 16, and even the quarter finals, to the detriment of having the most competitive tournament that the schedule will allow. Winning the Champions League is a great achievement, arguably the pinnacle of club football, but most champions still don't really prove themselves, as they would in a round-robin league format.
Just to note: above I have given examples of specific teams, but the names don't matter. In 20 years time we could have a set of slightly different top teams and them still leaving it to complete chance whether they meet or not in competitive football. The point is that we have all this European football and we leave it to complete chance, to the fine margins that a low-scoring game like football is built on, whether the best sides in any given era will actually compete against each other in pursuit of glory.
The Champions League structure made sense in the 90s until really the mid-2000s when there was wider pool of top sides and the champions of many of the second tier leagues were able to be more competitive, but not now. We have had one team, just one, from outside the Top 5 leagues make the CL final since Ajax in 1996. But we can go further still, since Porto won it 2004 beating Monaco, every single final, including the upcoming one in 2021, will have been contested by clubs proposed to be the founding 15 in the Super League (note: now is a good time to point and laugh at Manchester City who are the only one of these sides to actually reach the final yet in this period).
So we have a situation where the Super League teams have a stranglehold on the Champions League final anyway, but we still have a format that doesn't necessarily ensure that the best teams, proven by their results (and even XG!) domestically and continentally over a multi-year period, actually directly play each other to give us a proven champion.
Personally, I like UEFA's reforms, but don't actually feel they go far enough. I'd go further and greatly increase the number of teams in the CL. As well as increasing the number of berths for the top performing associations, I'd have more places guaranteed for national champions of leagues further down the association coefficient ranking. Currently 11 are guaranteed a spot and a further 4 can qualify. I'd guarantee at least 20 and let furthers qualify. The beauty of a Swiss-based system (or similar) is that it can be scaled easily and the format does the heavy lifting of sifting teams after the initial couple of rounds to get teams playing against others with similar records. This will give you a diverse set of matches early on, followed by stronger-performing sides facing each other and weaker-performing sides facing each other. If the Croatia champions are strong one year, then they will win matches and be paired against other winning teams. If the Hungarian champions are out of the depth against the stronger sides, they will lose early and be matched against other losing sides. There's no need to seed sides (unless you want to do an Accelerated Swiss), as you don't have to protect your commercial draws from being eliminated after a game or two.
I wouldn't at all be surprised if the tentative plan is to get the Swiss system through the door, allow the format to demonstrate its merits, before merging European competitions together.