Assuming you will get called with AA,KK 100% of the time, QQ 90% of the time and AK 50% of the time, the all-in push with AQ or 33 seems like a super donk move to me. You are only getting called by better hands the vast majority of the time. Chances 1 of your opponents holds AA is roughly 1 in 24/25, so 3 in 24 for AA-QQ and include AK...it means you can get away with it roughly 8 times on average to pick up basically nothing and be in a coin flip situation at best.
If on the other hand you are pushing AA/KK in hopes KK-99 or AK/AQ calls it is also a super donk move. You will be dealt AA once every 221 and get called say 1 in 8. So add in pushing with KK/QQ your looking at 1 in 70ish.
So every 70 hands you get to push your 3k to pick up 100 and 1 in 8 you get called with roughly an 80% chance to win, slightly less when you push KK and run into AA or AK or you push QQ and run into AK. So you win 700 outright and 2400 when you get called pushing your premium hands. So with the best hands you can be dealt AA-QQ, you double up once every 8 plays.
Now granted the numbers I put out are speculative. This not mathematics, just guess work for the purposes of discussion. I simply do not see how the all-in push is profitable on either end. If you have a marginal hand, you are only getting called by a hand that beats you and if you are pushing with a premium hand you are not getting called often enough to make it as profitable as having played for a standard raise and getting more money in postflop.