Internet access used to be billed by the minute back in the Prodigy/Compuserve/AOL days, and early phone plans mirrored that for ease of marketing.
Dedicated Internet wires came much later, and then the dedicated phone lines were dropped as voip was better quality and cheaper compared to the dedicated lines.
While the phone still had a dedicated line it didn't actually need a power connection, as the power through the phone wire was sufficient.
AOL was offering free minutes because it was an ISP, not because it was an online service. (It was also an online service. Most of that service was indeed free; some of it billed by the minute, but that was separate from the rate you paid for connecting to the internet.)
The telephone network made the utterly bizarre choice to intentionally degrade the audio signal of a call, guaranteeing that people would have an unnatural, distorted voice if you spoke to them over the phone. There was no way for voip not to be better quality.