Sigh. Saying lossless networks don't exist, is disingenuous. Some paths on some residential networks to some providers really are essentially lossless.
I have seen the Dialogic white paper. It's obviously biased, since they're still selling their fax stuff they created back before they were bought by Intel and all the really brilliant people cashed out and left. Surprised me to see a 2011 copyright on it. Same paper was out over ten years ago. If you note carefully that they turned off ECM and put a vague (paraphrased) "with ECM completion rates were higher but the image was [in Dialogic's view, but not quantified and no examples shown, of course! because in many people's view the quality would have been fine for a simple document] unacceptably distorted".
If you look back at my sentence about Nyquist it's specifically talking about the resulting output of a lossless codec. Sampling at 8 KHz means absolutely bupkis if you're going to stuff it through a lossy codec instantly thereafter. The point was, that sampled at 8 KHz and left alone, fax tones will pass adequately through that, just fine.
Shoving that lossless codec through a packet loss filled network, sure... that'll suck.
We can sit here and quote textbooks all we like. The original question was, "Can I hook my fax up and have it work on a typical residential VoIP provider. And the answer was a complex... Maybe. And that's still true.
Your provider needs to not be using a lossy codec and/or you need a handle to pull to "change the voice quality" as an end user. Some providers are conscientious enough to provide it. They usually call it "bandwidth saver" or similar. All they're doing is telling their gear to negotiate G.711 on the high end of that end user setting for high bandwidth. (No one is offering it commercially as a residential service, but the so-called "HD" codecs will happily pass fax also. Typically only seen in business service on private networks, since carriers are cheap. Better audio quality than the old PSTN is not a goal that any residential provider usually shoots for or offers, since their head end bandwidth requirements go higher and their bottom of the barrel commodity prices won't allow them a profit using those.)
As far as the snarky "show your work" crap, it's an aviation Internet forum and the replies are tailored to the question. I'm not writing a damn engineering document explaining 20 years of VoIP to answer "can I make my fax machine work?" Kinda stupid waste of time, honestly. Folks asking "Will running my O-470 work LoP?" have the same types of never-ending threads come up, and the conclusion is always similar... "Go try it. Maybe. Some do, most don't. Not designed for it."
A scanner and an email is far smarter, but some businesses still think fax machines are the cat's meow. And Courts strangely still accept them over most digital documents, but that's been rapidly changing for a number of years now.
Best advice: Dump using the fax machine. But that's not the question the OP asked.
Second best advice: Let some other idiot go broke building bulk faxing tech (the money went out of that industry a looooong time ago, but it was fun back when bulk faxing investor relations documents Net'd $10M a year as a side business... Yeah, Net. Not Gross.) and use their service, but you'll have to pay a little for it. Inbound they receive and email to you, outbound you scan and send to them and they fax it. Basically let someone else pay to maintain the history museum. Heh.
Last resort advice: Set your "bandwidth" or "voice quality" setting as high as it will go on a commercial residential VoIP vendor's user interface and try it. The quality will probably be acceptable for one-off faxing when someone thinks they need you to. Force the fax machine to 9600 baud in the menu and ECM on and give it a shot. It often works.
Dialogic paper was a nice touch, but like I said, they're horribly biased. They're still selling cards they designed in the 90s. They did new versions of them to replace components not available after RoHS, but they're not innovators anymore.
(Side note: Want to see a disaster of BER? Install multiple Dialogic T1 cards in the same computer and feed them from different carriers and ask Dialogic how to make the clocks line up. Heh. They're not carrier class and never will be. But, they're cheap and meet the 80/20 rule for things people buy their stuff to do. Similarly early Cisco stuff was a clocking disaster too, but at least they invested in telecom engineers to clean up their crap eventually... with an appropriate increase in price tag...)