Yup, there may be some handling issues with unusually wide tires, but you might not encounter that problem riding a bike with rims having a 21mm inner width. Most folks won't do hard, fast curves and cornering on a bike with 40-50mm wide tires.

I just went from 700x23 to 700x25 tires on my older road bikes 14mm inner width rims. Mostly I wanted to tame the chatter and vibration on rough chipseal. The bike was originally equipped with 700x18 tires, many years ago. It handled fine with 700x23, tracking like it was on rails on curves. But the past week it's felt a bit squirrely on curves with the slightly larger tires, which just barely clear the brakes. Even if it could squeeze in 28 tires the handling would probably be awful.

Handling may also be influenced by tread, especially pronounced tread on shoulders. Shouldn't be an issue with slicks or tires with very shallow tread/sipes.