It is an interesting thought. Has the Seattle Sounders success in the US Open Cup and CONCACAF Champions League and maybe even in the regular season hurt their chances in the MLS Cup Playoffs? It is not just about the minutes played by key personnel, or about non-injury based squad rotation, but also about how they use the salary cap.
Considering the amount of injury rotation and the difficulties in classifying how other teams "go for it" in various tournaments let's narrow this theoretical discussion to a few teams in the Designated Player era, specifically those which have won trophies and see how many of these used one of three techniques - Make the Playoffs and Hope for Success; Strong in MLS Competitions; All the Trophies.
This chart lists the teams that have won a trophy (not the V-Cup in Canada) from 2007 to the present;
The break at 2009 is to recognize the shift from the Beckham Rule to the Ljungberg Rule allowing up to three DPs per team. Those also aren't the only successful teams. An argument could be made that the "other" Conference champion matters as it is a path to the CCL and the rare Allocation Money for success. Let's add those in, as well as a reminder of the regular season success of the MLS Cup winner;
Our first note is that the MLS Cup winner is evenly split between "Good" regular season teams and "Decent" ones. But at least one (LAG '12) of those "Decent" regular season teams and two (LAG '09, RBNY '08) of the Cup losers were gunning for the regular season title as well.
The LA Galaxy place a lower emphasis on the US Open Cup than some teams, but not much. Landon Donovan travels to Starfire to play in that tournament. Considering his relative health, age and Bruce Arena's hatred of artificial surfaces Donovan's participation is not because the Galaxy don't care about the tourney. In fact outside of the earliest of rounds LA puts out lineups that show up in regular season matches, not Reserves. Now, they do play predominantly Reserve lineups in CCL matches to lower their travel burden. Still, their Reserves helped them qualify for the CCL Quarterfinals twice in a row. Yes, they've won the MLS Cup twice, the Supporters Shield twice, a solo Conference title once and so it looks like they are just an MLS targeting team. That would be wrong. Arena uses his personnel to win games, no matter the tourney.
Kinnear's Houston Dynamo are underrated, but quite good. Twice in the DP era they've earned a Conference Championship, just short of a Shield and could be considered as a team that only goes for it in MLS play. Except that from 2007 to the present they've also made it to the CCC or CCL quarterfinals three times. In the Open Cup their best 2007 to present season was 2009 when Seattle knocked them out. But that lineup? It was pretty good, so was the one they used to crush the Battery in the round prior. Their other seasons were similar.
Columbus worked their magic under two different coaches and their success was during that transition. You know one of those coaches rather well - Sigi Schmid. He did a lot of things with which you are familiar. His protege, Robert Warzycha, continued those same strategic elements and the tactical tweaks are significant over time, but not in 2009. Twice they made the CCL knockout rounds. You may remember facing them in the Open Cup Final.
Teams with limited success
One could say that Real Salt Lake used the "Just make the Playoffs and Hope" path in 2009. They did well with that. They then shifted what they are trying to do. They try. They came darn close to winning the CCL. They bought a home game in the Open Cup, then lost.
Dallas and Colorado definitely rolled the dice. One won, the other lost. San Jose, they wanted it all. D.C. United want it all, they just aren't good at it lately. New England used to be really good, but the DP era changed things for them.
In the DP era four teams could be considered in the category of "All the Trophies." RSL is the worst of these and they have a strong record and are expected to be strong again. The Galaxy are the best at it and probably will be good at it again. Houston and Seattle are both model on-field franchises that any team but LA would be happy to be.
Is it possible to focus on just one tournament, or just the MLS matches? Sure. Would that ensure success? Absolutely not - look at Portland, Chivas, New England, New York, Philly and see what that does.
When you fall short in that path you have at best a decent season, at worst you are among the worst teams in the league. If a team goes for all the trophies (TFC belongs here with LA, Houston, Salt Lake, Seattle) even the failures are rather successful.
Maybe this is self-defining, as the teams that aren't good don't qualify for more trophies and good teams do. But the fact is more Allocation Money for good teams is only available by being among the best in three different tournaments. It is the only path to retain those players that helped the club be good in the first place.
Could one theoretically blow off a tournament or two and succeed in a third or fourth? Sure. That theory just eliminated the chance at greatness.
I kind of like greatness. To quote Queen, "I want it all. I want it all. And I want it now."