will an old wheelset support 28mm (28c) 700c tires or will they "balloon"
Wider road rims have become more popular, in part because of the reasons you're talking about, but 28 is far from the reasonable maximum for a more classic 19-20mm road rim, and will be totally fine. Consider how many people race cross on 19-20mm clinchers with 32s and 35s. Where the actual line is of what's reasonable is a hotly debated topic that there are other questions about.