I was going to wait a little longer to make this post but it is a good enough time for it I guess.
I'll discuss all the different options that we have and the merits of each. Dealing with Post flop, we shall assume we miss the board because this is the most likely outcome. We have no suits, Straights are not too likely and when we hit, it is easy to play. It is when we miss that makes it difficult.
1) Folding. It is pretty bad to fold AAxx preflop seeing as you are almost always a favourite. Yes you are only slightly ahead but in a cash game you have to play small edges to make the most profit.
2) Pot. Potting in my opinion is probably the second best option. The reason that potting is not the best option here is because we seldom get all the chips in preflop. A competent villain at this stakes is not going to stack off very often preflop, even with hands like J-10-9-8 double suited. Most villains will often just call the 3 bet (which would be to about 1.50$ if my math is correct). Say everyone comes along which is kinda unlikely, we have a pot bet left to get the money in on the flop but against so many villains, if an A is not on the board we are generally behind here and most likely end up check folding a TON of flops cause bluffing into 3 or 4 players is pretty aweful.
If we can pot and get it HU against the 8$ stack, which is the most likely situation with a 3 bet, he still has 6$ left and a pot of only 4$. What do we do now on the boards that miss us? In a situation like this, villain hits a lot more boards than us (if he does not have AAxx as well which we can safely disregard because he would have stacked that preflop). Do we pot? Is it profitable? This is a situation where we are way behind or slightly ahead if an A is not on the flop. We pot and he shoves we have to call when we are crushed unless he is spew tard. We check and he bets, we are left in a crappy position. When he folds to our c-bet, he is folding every hand that we beat.
It is only correct to pot in this situation when we can get the majority of our stack in preflop so that we can just shove on the flop, which makes decision making so much easier. If by potting you can only getting about 20% effective stacks in preflop, you are just going to find yourself in a bunch of shitty situations. A lot of people forget how much of a post flop game this is. Ill just use an example, We have AAxx, villain has K-8-7-6 double suited. What do you think our equity is HU preflop? We have a whopping 52%. When we stick like 30% of stacks in, when he misses he can safely fold a lot of flops without much decision but when we miss, a)we lose a ton of money, b) we sometimes have to give up and allow him to bluff us out of the pot, c) we check and he checks back and now he gets a freecard which is more likely to help him that us.
Plain and simple, if you cannot get it in preflop or 75% of stack preflop, it is probably a bad pot bet.
3) 3/4 pot, did not really consider this cause it leaves us in the same situation as potting does, with a little bit less money committed. We also keep more villains in and have to give up more post flop.
4) Calling. Lose less money when you miss. Disguises your hand more. Can give up a lot easier and have less tough decisions post flop.
Hope this makes sense, seems like I'm ranting a little.