Compartmentalizing workers from each other and from customers is a means of control. Specifically management is trying to make sure that their developers do not get exposure to internal or external groups that may try to hire them away. Or give them a job if they get fired or laid off.

Consider

Case A: Customer knows you well understands you are competent. If you want to leave or are laid off that customer might eityher hire you or know someone who does. Or at least will give you a solid reference.

Compare with.

Case B: Customers and others only know you through your boss.

I dunno, I am certainly not hidden from our customers; I interact with them directly, every day, over email, phone and screen-shares. But other than rare on-site visits and conferences, I don't see them face-to-face, so it doesn't much matter what type of shirt, or even any shirt at all, that I'm wearing.

At one place, we kept suits / formal office clothes in the closet for those times. No need to make it a regular thing.

On the other hand, at one place I worked it would have been illegal for the customer to interact with us in our office space, but we still had to wear formal office clothing.