Can be important for anyone with client contact. Even if you don't care what people wear, external clients will react differently depending on what you wear. It could be that you specifically don't want to wear suit to give the impression that you're a dynamic start-up but in the end clothing always matters.
Programmer is rarely a client-facing role and I think the odds that someone overdressed can successfully dress down, if requested, are a little bit better than the opposite.
Depending on your position it might also be different for different clients. My friend kept a suit at work in case they had to meet with the feds or a bank.
If I ever wore a suit to work, my coworkers would be wondering what was wrong or who was visiting.
Exactly, being overdressed can be as bad as underdressed. If everyone expects you to wear jeans and t-shirt, a suit can be as damaging as not wearing one when you're expected to.
I would be bothered that someone dressing excessively formal might act excessively formally - after all, dressing formally is normally a deliberate display of conformity.
It's not an act of conformity in that context, but it's usually an act of conformity. The most likely explanation I can see for someone dressing formally in an informal environment is a habit of conformity coupled with an insensitivity to change in social environment, neither of which seems like a desirable quality.
How is it any more a habit of conformity than wearing jeans and t-shirts, especially when the set of workplaces where wearing suits is the norm is smaller?
True, but only if they repeat it more than a couple of times, after they have had time to take on their environment and adapt! (or if a new graduate, afford clothes that fit the 'new conformity' of the particular office casualness...)
I dressed up nicely because I wanted to pay respect to my interviewer, they made an effort to be there, I wanted to show that I cared to make an effort too.
Why would you be bothered about what someone wears at work - formal or informal?