For US airports, is there really a difference between printable boarding passes and mobile boarding passes?

There is one reason I can imagine - if it is an international flight, they are required to check your documents to make sure you are allowed to enter the target country.

Many airlines do that by writing 'docs ok' or some other shorthand on the paper boarding pass (some use a stamp, as once you know the method, you could just write yourself 'docs ok').
With a online boarding pass, they cannot write that on the paper. That could be the reason they require paper boarding passes.

I have seen the same with Lufthansa flights to Europe from Orlando and Newark; if you use the mobile boarding pass, they ask you for your documents (again) at the boarding door (more or less annoyed).

Yes. Printable boarding passes work. Phone boarding passes are unreliable, because they require you be logged into the airline "app" and that login expires for security reasons. Or the user has to find his email. Or the user cant get WiFi and for some reason the process to get that BP requires it. Or the battery is flat.

On cell signal, airports are a relatively good case, since they are open, airy, spread out and on the surface. I can tell you in the bowels of Union Station, cellphone signal isn't a possibility (which also means the free wifi on the train cars has no uplink). Amtrak had not thought to extend wired WiFi (least of all free Wifi) to the platforms proper. As it happened, I had the foresight to shoot a screencap of the boarding pass, and I switched to my photos app and presented the screencap.

Anyway, back to our airport. You will have quite a lot of tech snafu's like this. Forgetting their app password. Frantically searching their emails. Or their battery dying. Or whatever. People being peolle, this wont happen in the queue, it'll happen when they are talking to the agent. And it really, reaally slows down the line. To an airline, flow is money. If you require printed tickets, all that is solved.

My guess would be simpler: paper is faster to scan during the boarding process.

TSA certainly isn't going to be the issue here, by the way (they'll let you in; they probably don't know the individual airlines' policies, at least the individual agent likely wouldn't); it's the gate agent who'd have the issue with it.

While much of the time phone screens are fine, sometimes they just don't scan; they take an extra 30 seconds to a minute sometimes to scan for people whose screens don't have sufficient contrast or brightness, or whose phones are overly smudged, or don't have it up when they get to the gate. Paper will be faster on average, so they may well be simply disallowing them to speed boarding.

It doesn't answer the broader question, but at least in this instance Air Canada agrees that there isn't a difference:

Transcript of screenshot

Q: Is it necessary to print the boarding pass when departing Las Vegas airport to Vancouver? Or can I just show it on my phone screen?

A: Hello you may definitively have your eBoarding Pass on your cellphone. /Alex

So its probably an issue with their site not being up to date.

It's Air Canada's aeroplane, so they get to make the rules about who is allowed on board. If their rule is that you don't get on without a paper boarding pass, then you need a paper boarding pass if you want to fly. (Other answers have explained why they might want to make such a rule).

For U.S. airports in general? No, there's no difference and mobile boarding passes are definitely supported. TSA won't care and likely hundreds of thousands of people go through TSA security with them every single day, including at LAS. I've being going through TSA checkpoints with mobile boarding passes for years and it's never been any trouble.

If there is any difference, it has nothing to do with US airports in general or TSA, but only Air Canada and possibly only Air Canada at that particular airport. If there's any problem, it would be with Air Canada scanning your boarding pass at the gate to board, not with TSA scanning it to enter security.