Hello. The MLS salary cap does increase. I recall it going up every year so far (I am in 2021 now).
It took me a while to reply with an example of an increase because of where I was in the season when I saw this post.
In a Seattle Sounders save, I received an email on 26 December 2020, stating that the salary cap will be increased for the upcoming 2021 season to US$4.18 million. The minimum wage will go up to $62.4K per year, and developmental players will receive $51.66K per year.
I am not sure to what extent the league reputation affects this, since I have no other MLS saves to compare it to. The MLS in my save is currently a 3 star reputation league, up about 1/2 a star from 2013 I think.
I am enjoying the MLS a lot, and the increasing salary cap does help relieve the constant wage pressure. I don't know if others have experienced this, but one irritant is that the transfer offers from AI MLS teams almost always start at $300,000 (which thankfully can be negotiated), and it is very challenging to get high quality coaching (my best are a couple Americans, and some S African and Mexican coaches) -- none are over 4.5 stars in spite of many rounds of poring over lists of names hoping someone good would pop up... Cheers!