The alloy rims that can be found these days are just not going to be as wide as the old steel ones.

The only time this is a problem is with the older double-sided cables (if you are still using them) because the brakes are not going to reach the rim with those old stock cables because there just isn't enough adjustment. You can shim the brake shoes out with some types of pads that have a female socket in the pad (like the Avenir Sticky-fingers pads) and a longer bolt. Or just replace the cable with a modern cable and a knarp which gives you more adjustability.