I have never had any trouble buying new audio tape (1/4, 1/2, 1", or 2" widths). Lots of studios still record in analog, and lots of artists specify analog recording. Some even insist on analog mastering, too. Digital is easier, but the analog sound is the key reason for using magnetic tape & Ampex or Revox (or Studer) recorders.
I buy tape from US Recording Media (
http://www.usrecordingmedia.com), with whom I have no connection. I generally use Quantegy Grand Master 456 tape, the same formula as the old Ampex mastering tape from the 70's. Most of the better decks had bias settings for this tape, so you could just load & go.
The end of open reel tape is not here yet, and is not coming as far as I can see.
I don't use audio cassettes, but I see a full range of Maxell & Quantegy tapes still available at retail outlets...Frankly, I think that audio cassettes have little to offer, so it just might happen that we will see NOS cassettes on eBay in 20 years!