I'm in the process of removing an old telephone jack that has wiring running along the wall. The jack is easily removed, but I'm unclear on what to do with the wiring. It seems short sighted and foolish to just snip it off.
On the other hand, the wire seems to lead into the crawlspace below the house, and I'd rather not go under if I can avoid it.
If you are removing it, remove it.
It's only "short-sighted" if you have any conception that you might want a landline phone there.
You MIGHT be able (depending on how snug it is, and how many layers of paint are on the cable making it fatter) to just stuff the (uncut) cable down the hole in the floor once you have it unstapled.
But simply snipping it off is perfectly reasonable under the "you never envision a landline in that location, or perhaps anywhere in your house, again" premise.
Even if you never have a landline, you might want to use that wire again. I have repurposed old phone wiring for many things = thermostats, alarms, doorbells, etc.
If you really don't like looking at it, you could clip it off just above the staple above the baseboard. If you ever need to re-use it, there's enough to work with.
I would terminate the cable in a screw terminal surface mount jack on the baseboard.
These jacks are very inexpensive, readily available, and can be installed in just a few minutes without any special tools. If someone ever wants to repurpose it, they can use the jack or extend from it by splicing on the screw terminals.
This way if you or someone else in the future ever wants to use that wire, you can easily splice on at the screw terminals and extend the line where ever you want.
Cut it off at the floor level and push it down; out of sight, out of mind is applicable and safe in this situation.
If you are sincere in regards to your question title:
What's the right way of removing an indoor telephone line?
then get in the crawl space and cut it back as far as you can.
If you can find the other end of the cable (where it connects to the line coming in from the road) and disconnect it before you cut through the cable, that might be a good idea.
That way if the cut end of the cable is ever shorted for any reason, it wont render all the phone jacks in the house useless. You may not need the phone wiring for anything, but it might come in useful for somebody down the road and a hidden short can be a pain to find.
Plus it's never a good idea to cut through cables unless you're 100% sure that they're dead and no idiot has hooked them up to something they shouldn't have.
Land-lines have been on their way out for years now. It may be prudent to keep at least one telephone jack working, but there's no requirement for a phone handset in every room of the house. I don't see any point keeping the jack.
While it is theoretically possible to use telephone wires for Internet, basic telephone wire is terrible, and leaving it in a crawlspace for decades hasn't helped; you're better off just using WiFi. In general, I'm unaware of any actual uses for a telephone wire that aren't telephone-related.
Leaving the cable in place may be useful if you plan to replace it with cat6 at some point. (Basically, tie the cat6 to the end, and pull it through from the other end. That way you can get a cat6 cable in place without going into the crawlspace.)
