I changed out the stock alloy 27" wheels on my '73 American Eagle Kokusai (Nishiki International) because the spokes were brittle/breaking, and for the aesthetic reason that icepick just mentioned.
I found and used a super-nice pair of Araya steel rims on Suzue hi-flange hubs. These rims (bare) are like 760 grams each, versus the wide alloy rims ~500g, so at least a pound was added.
The bike doesn't take fast, bumpy roads quite as well now, but the steering gained a solidity that is almost Schwinn-like now, which gives better tracking along roads with narrow shoulders continuously abutted by drainage trenches.

The geometry of a frame really affects how well that any particular handlebar and stem length works out. The ~70-degree head-tube angles on the electro-forged Varsity/Suburban/Continental frames gets along particularly well with upright "touring" handlebars and very short stem extensions, which Schwinn seemed to understand better than just about every other bike company(!).
I've never put a rider on an old Suburban/Varsity with upright handlebars without hearing very-positive feedback afterward. It's one of the ultimate cycling experiences.

On the other hand, I somewhat cringe whenever I see a quick-steering racing frame fitted with the sort of short stem and/or taller and swept-back handlebar that promises too-quick steering.
The angle-finder is my best friend when it comes time to selecting/fitting a bike to a rider and selecting an appropriate bar/stem combination!
Just as when I first found digital calipers to be super-affordable, finding a reliable angle-finder for $20 or $30 was something for this cycling enthusiast to get excited about!!