@Kuro466 You are sadly miss informed. I have friends banned from Blizzard games and they can no longer use the same mobile number as an authenticator for the account. Btw depends how each company uses the authenticator. Blizzard just notifies you when someone logs in with your account and when that happens it sends you a secure code to log into the game (that is how it works now in 2019) but it did not work the same way back in 2012 when they heavily promoted it.
R6S has an authenticator that does not allow you to even login to the account unless you type the code they send you in text message to your mobile. That authenticator literally will block the whole mobile if you cheat (the DEVICE NOT JUST THE NUMBER). That is why when you apply for it they explain it very clearly that in case of theft you have to use 4 specific codes and send them in the exact order you received them to an email address (along with other form of identification) in order to "release" your mobile device from their logs so that you can be able to re-use the same service and play the game. They keep the IMEI of the phone on their servers, not just the number.
CS:GO Prime did reduce the cheaters, because cheaters do not use mobile number to authenticate the account, because if they get banned they also ban their mobile number and device along with their email etc.
It is different for every company and depends how they use it, but it can be used 100% for reducing cheaters as it has been by Valve and R6S coming this year (2019). It is actually great at getting rid of noob script kiddies which are probably the majority of the cheaters anyways. That combined with hardware id bans, region lock and lawsuits against the cheaters will decrease the cheating dramatically.
Anything that reduces the cheating is better than doing nothing.