Yes, there are situations when you want your opponent to have AA. This is one of those situations.
I will only play 44 or lower if in late position and there hasn’t been a raise to me. Otherwise, those are –EV hands and should be folded. If you spot someone playing pocket fours or lower in any other situation, then you can make a mental note that they’re likely a weak player.
If I’m holding 55 or higher and I know my opponent is holding AA, then I’m smooth-calling. Obviously, I’m way behind at 20%, but if I hit my set, I’m getting all of my opponent’s chips. If I have fewer chips than my opponent, then I’m doubling-up. If I miss the set on the flop, I’m folding. It’s that simple. This keeps my risk low and my winning potential high, which is a great business proposition.
As a side note, if someone raises you pre-flop and you’re holding a low- to mid-pocket pair, I would not recommend re-raising. This can lead to a shove by your opponent, which can then lead to you folding or being pot-committed. If you fold, then you wasted chips (bad poker). If you’re pot-committed, then you’re not folding on the flop, but you’re likely way behind. That’s also bad poker.
You would prefer your opponent to have an over-pair vs. a drawing when set mining. If they have an over-pair, they will have a very tough time letting it go. If they’re holding a drawing hand, then you could have to fade draws. If your opponent hits that draw, you can be beat, but I’m still never going anywhere when flopping a set.
Set mining can be very profitable. You will usually miss and fold on the flop, but that’s why it’s called mining. When you strike gold, as in flopping a set on the flop, you’re going to double-up or take all of your opponent’s chips when they’re holding an over-pair.