I don't think you can take this conclusion based on the quality and competition present in one league. For all the talk about the PL's competitiveness how many titles have title contenders won in the past 10 years?
It's a flawed argument.
I'm not arguing about which league is more competitive than another though, nor the competitiveness of the overall league. Rather that being involved in a competitive title challenge in your league probably helps in more cases than not of CL winners. Of course there will be teams that will also be involved in a competitive title challenge but don't win the CL but that's probably down to another team being better than them so other factors will come into play and I don't think any title win/cup win is down to one factor but multiple.
In 07/08 when United won the CL there were 4 points between the top 3.
08/09 when Barca won the CL they won La Liga by 9 points.
Inter in 09/10 won Serie A by 2 points.
10/11 Barca won by 4 points.
Chelsea in 11-12 came 6th (Major difference to most of the recent winners).
12-13 Bayern won by 25 points (also only lost 1 game) (Another major difference).
13-14 Madrid were 3rd but 3 points behind the winner.
14-15 Barca won by 2 points.
15-16 Madrid were 2nd but a point behind the winner and 2 ahead of 3rd.
16-17 Madrid won La Liga by 3 points.
17-18 Madrid were 3rd, 17 points behind the leaders.
18-19 Liverpool were 2nd but a point behind the winner.
So that's 8 to 4 in terms of relative competitiveness of the title race compared to teams that won it by either dominating their league/performing poorly in their league but winning it. As I said before, I think that competitiveness probably is a factor in most teams who win the CL but it isn't the only one. Of course there will be elements of luck or a team being very very good in their own right without it mattering how other teams perform and other variants but the competiveness on all fronts probably helps in some format and translates across all competitions.
I think that if teams like Juventus/Bayern/PSG want to win the CL then it would probably help if their own league was a bit more difficult to win than it currently is. The competiveness they'd face in that could help translate into more competitiveness in the CL.