The arguments where people bring up their elo won't change much they'll just bring up their league level instead.
And people who do that are pretty stupid anyway and it'll usually barely slow them down when they find out you're higher. I've had many arguments with people where once logical arguments are failing they bring up their elo and I'm like oookay I didn't even bring up elo but you're several hundred below me, at that point they either attack you saying you dont deserve it or they say you're lying or brush off the importance of elo even though they brought it up, or they run away crying I doubt having leauges will change any of this much.
Anyway it seems like they major changes are it'll be harder and more grinding to get up most notably due to promotion matches. However its also much harder to drop out so that will atleast help prevent the 200 elo drops in one night because you're in a bad mood personally and I know other people who have done the same.
Basically I feel like people should more consistently be closer to their "true elo" as people called it.
Of course the otherside of this is its possible people who get elo boosted will take muuuuuuuch longer to drop down to where they should be.