In cricket, when a bowler is around the wicket, why does the batter not simply adjust their stance to counter the angle?

This would be a tactical decision by the batter. In some cases they might adjust their stance. In other cases they wouldn't. Factors for the batter to consider:

1. Is the batter left or right handed?
2. What type of bowler is going around the wicket? Seamer? Pace bowler? Spin bowler?
3. What is the broad intent of the batter at that point. To survive? To make quick runs? To get off strike to get the other better batter on strike?

So this is where tactics, especially at the professional level of cricket, get interesting. So here is a contest between a skilled batsman and a bowling genius, Shane Warne. The batsman adjusts his stance and Warne by going around the wicket sets the batsman up with a plan. See this YouTube video: Shane Warne bowling. Notice how the batter uses the defensive tactic of padding up; because the chance of getting out lbw is reduced by Shane Warne going around the wicket the batter can let it hit his pads. p.s in the link skip to five and a half minutes in. That is where the balls are all shown in succession.

It depends on what the bowler wants to do, We can guess/pre-medicate what the bowler is going to do by the field he set for you and what the situation of the game is.

For example if you consider a test match cricket where a right arm fast bowler comes round the stump for a right hand batsman, has a short leg and leg slip and a square leg, that mean the bowler is going to bowl short and into you ribcage expecting you to play the ball, if you open your stance you are setting up to play the ball which is what the bowler wanted to, you playing at athe ball instead of leaving or ducking.

When you consider the modern day format like T20, a right arm fast bowler comes around to right hand batsmen, to cramp the batsmen for the space he can create when the ball is coming into him, and if the batsmen want to open up his stance to a more open body approach he'll only give the bowler more advantage as the bowler can hit more area of his pads and has a greater advantage to getting him out LBW or Bowled.

Not only that opening up the stance mean you going out your natural way to counter the bowler. which your not used to that much, and have greater chance of committing a mistake, also you are not likely to score runs on the off side of the wicket if you open your stance as it is hard to play when your body weight is on the legside of the wicket

So that is why most of batsmen doesn’t prefer to change there stance if the bowler comes around the stump to distract/put him off guard.