I’ve noticed that in many symphonic works composed after 1900, the brass, especially the trumpets, are often muted. Why is this? Is it because of the larger brass sections in modern orchestras? Does the composer not want the louder sound of the brass to overpower the strings?
IANA serious musician, but it seems like the main point of muting is to play around with the timbre of the instrument, hence all the different buzzy, metallic, fuzzy, wah-wah, et cetera mute styles.
It also, as the name suggests, allows you greater dynamic freedom in the softer end. And don’t forget that there are horns that are almost always muted.
Because otherwise the powerful brass would completely overwhelm the wussy little stringed and woodwind instruments. That’s what my music teacher told me, anyway 
In my experience in both orchestration classes and listening to 20th century much, much of the modernist energy they had was devoted to creating as many new sounds as they possibly could in the orchestra. Keeping the mute on brass instruments for an extended period really does change the colour as much as it does the volume.
Of course, this isn’t limited to brass instruments. You see greater use of pizziacato and “col legno” on the string instruments, as well as “scordattura” tuning (Mahler’s one of the first to do this that I can think of). And the amount extended techniques on the wood winds, from changes in tonguing to all the way to playing without the bell of a clarinet, variation really becomes the key.
If a group’s brass section is really professional-caliber, then playing very quietly - even unmuted - won’t be a problem for them. As others have said, mutes are specified more for their effect on the resulting tone quality, rather than volume.
I am an amateur tuba player, and I dearly wish all composers/arrangers would realize that removing or installing a tuba mute takes more than two seconds. (It depends how much clanging/crashing you’re willing to risk, I guess…)
That said, I don’t own a tuba mute. They’re surprisingly expensive, inconvenient as hell to carry around, and not called for very often. When one’s going to be needed I generally either find out in advance or at the first rehearsal (through which I just fake it), and then borrow one.
Plus they look like a silver suppository for an elephant.