I don't bike commute right now, but I have in the past. I always kept a spare change of clothes at the office (hanging clean in dry cleaning bags), and otherwise brought my clothes with me in a backpack. Neatly folded shirts, pants, and tie never developed noticeable creases on my ride, and a fresh pair of shoes and socks sat nicely at the bottom of the pack. I took care to ride easily enough to not sweat hard, and if I got pretty wet I would take it easy and slow for the last bit of the ride. When arriving at the office I would be a few minutes early each day to change in the bathroom, rinse my face and stow my riding clothes.
I don't think it's uncommon for people to keep a spare shirt and tie at the office for practical reasons, but I didn't want to be the guy keeping his whole wardrobe there. That would be a bit weird to me. I started doing things this way after seeing some people ride motorcycles to work. Most of them wore outerwear they stripped away and hung for the day, but many did not even do that in the summer heat.. they basically did what I described (keeping things in their backpack or saddlebag).