I bike commute 2x week a little over 7 miles one way. In the summer I wear shorts and a T-shirt and change at work. I roll up my work pants and shirt and carry them with me. I also take a small towel (one of those bright yellow microfiber clothes that come in the 100 pack at Costco) to wipe off any sweat. I need a shower when I get home but not in the morning. As long as you’re clean when you leave home you likely won’t stink all day.
In the winter I wear work pants (Business Casual) and (either sneakers or casual) shoes and change shirts at work. I have a light shell that I wear over an lightweight wool long underwear top when it gets below 40. I just roll up my work shirts. It’s worked so far (9 months of commuting). You will need mittens or good gloves when it gets cold. I also add some long underwear bottoms under my pants but I haven’t needed to yet (lowest temp was just below freezing so far). I wear a thin beanie under my helmet and down over my ears (one that is made of mid weight long underwear material).
I don’t really see the need to do the full lycra thing for 7 or 8 miles, but if some people are more comfortable that way, why not?