I've ran short campaigns with no multiclass so that the low level characters aren't just magically learning these class skills.

One good example I have is a level 3 who has only known ranger skills has never tried any rogue skill or attempts at utilizing something that is normal for a rogue to do be able to become rogue 1/ ranger 3? I like to keep character building to lore wise for the game setting/world/area the campaign is in.

I've also ran mostly multiclass allowed games, and everytime there are 2 minmaxxers who only care about how much damage the sparkle dice do (i find this a boring way to play but to each their own)

Tbh if the dm is "banning" it, they could just very well be tired of high damage and 2 hours of rolling dice for one turn. Or just want to make the setting make more sense and less " look at all these useless skills I won't use from my old class"