Possibly a bigger issue is having a place where they can work. If you've ever heard a podcast ruined by background noise, you know what I mean.
I think that musicians are particularly adept at mentally filtering out shortcomings of the audio "stack" when they need to, and hear what they need to hear. There are still seminal recordings that are only available as scratchy phonograph records and tapes made with primitive microphones. Maybe it's because we process music at a symbolic level. And it's possible to focus the lessons on the things that can be done remotely. By the time they reach college, they're already playing at an exceptionally high level.
A friend of mine who's a music professor at another university says that he encourages students to use "whatever works" including their cell phones, so that the mechanics of recording don't distract from learning music. They've always had to deal with issues such as students who can't afford professional quality instruments.
Of course they're missing out on ensemble playing.
With the violin, that place is probably above the fiddle, so you have to find a way to dangle your phone, or put a mic on a stand. Especially since you're probably standing to play, for reasons of good posture.
And you want the mic to be close, basically to drown out the effects of typically bad room acoustics unless you're lucky to have a nice recording room. Plus, noise from HVAC and other sources.
And... mainstream recording apps for primarily voice use have built in compression and possibly other artifacts that you have to figure out how to turn off.
And... if you want audio and video, it further constrains your options. You often need your teacher to see you play, to comment on posture and technique issues.
Once it's all working, then the mic in a cell phone and its audio input hardware are actually surprisingly decent. The tiny little condenser mic elements are fairly high fidelity, and an audio codec is pretty much a slam dunk nowadays.
Personally I don't like the sound of a close-mic'd acoustic guitar. Unlike cello and violin, there can be a lot of fret noise and wound strings can be quite squeaky. Classical guitars have different, quieter wound strings under less tension, and nylon for unwound. This is also to reduce fret noise and squeakiness, but personally I prefer the full sound of steel strings. I've been working a lot on getting my fretting technique more clean to eliminate all of that mess and sound more professional, but to be honest I actually prefer to hear my own guitar live in a quiet, resonant room and not through a recording. Bathrooms with tile are great, if a little small! Of course that sounds like complete garbage if you try to record it. But it is absolutely heavenly live :-)
For the doublebass I can imagine you'd be best off with a mic stand at a couple feet away and seeing if you can get a mic that has a very narrow response angle (almost a directed mic).
Cheers and happy recording.
When it was in person, you showed up, played, and were done, good or bad. As a performing musician, I greatly prefer to make a mistake in front of an audience than play perfectly into a microphone.