Combining Formats
If you want to reap the benefits of multiple formats while covering their weaknesses, then try combining them! I'll be focusing mostly on non-eliminating -> eliminating formats here, but there are all kinds of combinations you can use.
Taking a Page from Sports​
One of the most common combinations is something we've seen in traditional sports. "Regular season" followed by "Playoffs" is, in format terms, Round-Robin (or some variation of it) into Single-Elimination.
When the season is coming to a close, there are usually some competitors out of contention and their matches don't really have any impact (one of the weaknesses of Round-Robin). But, the playoffs that follow have the most exciting & impactful matches (a strength of Single-Elim) to cover for that.
On the other side, the playoffs would be unfair & weird if it were standalone; you might only see your favorite team once, and if all of the competitors were just dropped in randomly then we might see top teams knock each other out early (Single-Elim's weakness include having few matches and needing excellent seeding). So it's a good thing to have the regular season, because it gives far more chances to see our favorite competitors and it gives us earned seeds in the playoffs.
In this way, round-robin and single-elim blend together to cover each other's weaknesses and set up each other's strengths.
Applying to Esports​
No, esports don't have to be like sports, but we should still learn from sports and apply those learnings to what we do!
Round-Robin to Elim​
This traditional 'league' structure seen in sports is something we don't see as frequently in esports because of the resources involved with competing (and broadcasting) over several weeks. Therefore, we tend to see it mostly in scholastic esports (where school club infrastructure keeps teams together) and in premier franchised esports leagues (where $$$ & signed contracts keep teams together). Call of Duty League 2021 used a series of five majors, where each major consisted of Round-Robin groups (played over multiple weeks) progressing into a Double-Elimination "Major" weekend. That way, fans got guaranteed matches with their favorite teams (which were all determined upfront and scheduled/ordered for storytelling purposes) while also getting high-impact elimination matches at the end.
Swiss to Elim​
Swiss is more common in chess and TCG/CCG games than in major sports (although now we're seeing "the world's game" incorporate it), and largely found its way into esports via digital TCG/CCG videogames like Hearthstone.
When setups and space aren't an issue, Swiss is an excellent way to start an open event, like a Hearthstone event with hundreds of competitors at DreamHack. They combine the power of Swiss (a logarithmic-scaling, non-eliminating format) with a single-elim final. By doing so, they provide plenty of matches to all competitors, and deliver an exciting finish on broadcast, all in a timely manner.
But you'll also see invitational tournaments utilize Swiss-to-elim formats. The 2017 ELEAGUE Major (source: HLTV) used a record-threshold Swiss -> Single-Elim format where teams who won 3 matches advanced to the final bracket and teams who lost 3 matches were eliminated.
Other Miscellaneous Examples​
With the basic principle of "use strengths to cover weaknesses," you can come up with other combinations: