Honestly, I don't know how good as idea this is.
After the small ms period end, player would be very frustrated because they will have to handle an hard leveling up experience after, don't know, the 3rd or 4th badge.
Then the option would be 2:
1) You try to continue without MS but you are bored by the difference in the gameplay or you ragequit the game the very next day;
2) You shop another MS. But this.. would make people think this is a pay2win game.
An idea to help new players to not quit because of the leveling up, may be give them a 10/15% Exp boost until the win the 4th badge. 10/15% is not a huge difference like MS is, and should be presented as a "promo" for MS.