Out of respect for the many old rims out there, each with their own limitations, I have homed-in on a repair protocol over the last 30 years or so.

I set the two threaded pointers on my truing stand so that the rim can barely pass through freely. Then I tighten them both to the point that the rim gets grabbed at any excess variation of thickness of the rim, which lets me mark the span of the rim which has an excess thickness.

Using a very large Channel-Lock Plier, together with a thick leather toe strap or similar material, I position the innermost depth of the jaws upon the strap over the high spot.
I then move the plier's jaws so they are as parallel to the brake tracks as possible, and apply heavy pressure over a series of spots spanning the over-width area of the rim.

This sort of thing requires some experience to be "quick and easy", but even a beginner can have a patient go of it with little chance of damage if a gradual approach is used with frequent re-checking of the results.
I am often able to make defective rims as good or better than average brand new ones in terms of actual braking smoothness(!) with no lengthy searching for perfect rims and then rebuilding.

The narrow Araya alloy rims have a tubular sleeved joint which so often presents a bulge at the joint, but these are much harder to correct I have found. Fixing these is frustratingly difficult to achieve even partial remedy.

Many steel rims feel lumpy in response to braking force (Araya and Ukai steel rims seem smoothest), but this is much less of a problem at higher speeds.
So to a degree it is not an issue at all, and I totally enjoy riding my nearly-stock (though now 12-speed) '75 Varsity with it's original rims. A key is to use the right pads on these rims.