Not charging at idle.

Some model alternators simply won't "kick in" well at idle. This is complicated by the fact that rebuilders get sloppy and put the wrong rotors into the wrong stator, and come up with a poor performing unit. Also, some alternators are better at low speed. The so called "squareback" ones generally are better, and in particular I believe it's the 45 amp rated on is particularly good.

Actually, "back in the day" this was common. If you can round up another alternator cheap, even a used one to try, that might be worth a shot. Frankly most of us lived with it and didn't give it much thought

It also might be that you have a small capacity battery, and the load on it when not being charged causes it to drop sooner than a more robust design. This can be a just-plain small light battery, one that is aging, or one that has something defective