Maybe saves money on having to change the credits again with continued cast changes.
Doubtful, Jessie Spencer (Chase) and Jennifer Morrison (Cameron) had
very reduced roles in Season 4 to Season 6 (when Chase rejoined the team) and they remained in the opening credits. Morrison left the show in mid-Season 6 after two seasons of being not much more than a background character for two seasons and she remained in the opening credits all the way through Season 6.
Kal Penn (Kutner) joined the cast in Season 4 and never got to be in the opening credits during his two seasons on the show.
Olivia Wilde (Thirteen) and Peter Jacobson (Taub) were regular cast members from Season Four through Season 6 (though S4 was somewhat muddier given the shortened season and the competition to see who would get House's fellowships) and and didn't get in the opening credits until the start of Season Seven! They had large, prominent, roles on the show for nearly three seasons and they were listed with the guest cast in the start of the second act after the opening credits.
So, yeah, I doubt it's something to do with constantly changing the credits as, well, the've only done it once in spite of having pretty much constantly mixed up their cast over the last three seasons with regulars Chase and Cameron getting varied amounts of screen time (Chase went from a docling, to a background character and then back to being a docling.)
Given the time stamps above it seems the opening credits were removed most likely to make room for more ad time and, possibly, to reduce the loyalties they have to pay to Massive Attack for the use of "Teardrop." Though they still use a single chord from it for the opening title sting, but I'm sure the loyalties on that aren't nearly as high as they would be for using a good-sized chunk of the song for an opening sequence.
I just assumed removing the song was for more story time as over the course of the last six seasons or so whenever they had an "event"/"Sweeps" episode they've nixed the opening credits for what seemed like a bit more story time.
That 30 seconds can be quite a bit, that's a dialogue scene between Wilson and House in Wilson's office that clues House to the case, that's a quick clinic patient, hell it'd be a half-way decent whiteboard scene.