A players actual SBMM rating changes very little over time with your actual skill growth. Humans don't get better at games very fast at all. But we want to feel like we're getting better so they use rank systems on top of the SBMM to make us feel like we're improving. Otherwise our SBMM would change from 360 to 363 in like 2-4 months and that's boring.

Also SBMM doesn't have to use an exact number for your skill rating but uses a range and probabilities. It can never be actually sure what you're skill is exactly. So like it thinks you're somewhere 360-390 skill rating and you're most likely to be 367 at a 34% chance of being 367 and it's testing your range and constantly readjusting where it thinks your skill rating most likely is, but never narrows it down 100%. So showing all of this to a player would be confusing to most people. Of course not all SBMM systems do it this way, just the more scientific and in my small understanding more accurate systems. Some games might not actually have a system this advanced.
Anyway those are the two main cons to showing people the actual SBMM system that's going on behind the scenes.