Chelsea don't have any stars. Kante, arguably, but he's a tough tackling midfielder, not a world class creative player or goalscorer. Let's be honest, it's actually pretty rare for the Champions League winner to also win their domestic league (unless it's a one-team league). The difference with a cup competition is if you come up against one team that happens to play a style that exploits your weaknesses, you're out of the competition. And that's happened a few times, often combined with Pep recognising this and then trying some mad tactic to contain them, rather than imposing our regular game on them.
Yes and no. If you are mainly a defensive team, you don't need stars, only a very physical and tactically disciplined squad and manager, but we are not a defensive team. In the last 10 years:
11-12: Chelsea, defensive without stars (Drogba, Lampard and Terry were already way passed their prmes). Also, this was a miracle.
12-13: Bayern --> Robben, Ribbery, Neuer, Lahm (top 10-15 players in the world), Kroos and even Muller were top 30.
13-14: Madrid---> Ronaldo, Benzema, Ramos, Modric, Kroos, Marcelo, even Di Maria are all top 20-30 players.
14-15--> Barca: Neymar, Suarez, Messi, Iniesta, Dani Alves all top players .
15-18 ---> Madrid: same as 13-14 Madrid - Di Maria + Bale.
18-19 : Liverpool: Salah, VVD, Mane, and at least for this season Robertson and TAA.
19-20 Bayern: Lewandowski, Kimmich, Neuer, and maybe Gnabry, Muller, Davies.
20-21: Chelsea, mostly a defensive and well-organized team.
I am not talking about Messi, Neymar, Mbappe,Ronaldo type of star. But if you want to win offensively, you need at least 3-4 top 20-30 players in the world (with 2 being in the top 10-15).