OK - I'll take a stab at this.
MLB is trying to address the balance of pitching vs hitting.
in recent years, starters are throwing fewer innings, so they are going max effort all the time - i.e. harder to hit. then, teams bring in relief pitchers who throw 1 inning at a time - again, max effort, harder to hit. (look at the difference in Griffin Jax as a starter vs a 1-inning reliever)
hitters rarely get to see a starter three times in a game. instead, in almost every at bat, they are facing a fresh pitcher who is throwing harder with better breaking stuff, because they are going max effort on every pitch. (which is also leading to a higher rate of pitcher injuries - but that's another topic)
so, by imposing a 13-pitcher limit, teams will - theoretically - have to extend their starters for longer outings, or have relief pitchers throw multiple innings. either way, hitters will (hopefully) have more opportunities to bat against pitchers who are not going max effort on every pitch, or are getting tired at the end of their outing and becoming more hittable.
we'll see what type of impact it has.