Is QoS an issue for VOIP calls over the Internet?
Sometimes. The answer why is related to the extinction of these objects:
(for people born after the year 2000, that's a phone booth)
QoS is only an issue if the customer thinks it's important enough to pay for.
it's important to maintain QoS on an internal network (i.e. prioritize VOIP
In practice, many enterprise networks get away with no voice QoS because they simply don't have enough network congestion to matter (people's experiences with cell phones have made occasional voice blips acceptable).
On the other hand, service provider networks should consider deploying voice QoS where it makes sense.
My ISP says that traffic from their SIP trunks goes over their
QoS-managed network to the PSTN.
Indeed, many enterprise networks buy dedicated SIP trunks to the PSTN so they don't have to waste a lot of time managing complaints about excessive voice drops. This is what I recommended to my employer.
There are lots of 3rd party SIP providers. From a theoretical perspective,
I don't understand how they can ensure call quality.
You're right, internet voice providers can't give much control over call quality.
Yet the proliferation of these services would seem to indicate that
I am wrong.
Arguably, the proliferation of those services means that some people will sacrifice potentially lower call quality for a less expensive service. IMHO, many of those people are home / small business networks.
Background info about the phone booth comment
After the breakup of the Bell companies, there was a lot of competition for phone business; it was viewed as quite lucrative, because of the monthly revenue stream from it.
In those days, there were rigorous standards around delivering voice services, such as Telecordia GR-series standards. The end result of these rigorous standards and competition was that customers expected increasingly better voice quality over time.
Another point about this period, people kept spare change in their pockets and ashtrays to make calls on the road (in a phone booth, see picture above).
To some people that may sound strange, because you have a phone in your pocket; however, cell phones only started becoming common in the 1990s. Early cell phones forced people to start compromising their expectations for call quality; the portability and convenience came with a price... cell phone call quality was noticeably worse (some would even say "horrible").
This is no small point, until cell phones became common, companies could go out of business for delivering bad voice quality. However, as people used cell phones, their expectations for phone call quality gradually got lower. In a way, cell phones opened the door to those "internet voice providers".
Furthermore, the proliferation of cell phones made phone booths extinct.