How long would a all in one touchscreen desktop last?

AIO computers are nothng more than a laptop attached to a monitor. AIO also have all the same restraints as a laptop. As for reliability, only Mac (iMac) seems to have conquered that.
Touchscreens should have become more of a "thing", but most people like the keyboard/mouse better (you aren't reaching across your desk all day).

They take up less room because they are a modified laptop.
The touchscreen for most people is unused.
There's no published failure data for all in ones.
When either the screen or computer has an issue, the whole unit is broken as there's rarely an HDMI output on an all-in-one, though a few have an extra HDMI input for the display.

They don't do well at gaming typically unless very expensive with GTX 1050 or better graphics.
You can also get tiny desktops with integrated Intel graphics.
https://www.bhphotovideo.com/...details&Q=
https://www.newegg.com/...8H556W2908

All cheaper pcs seem to have issues faster.

And generally, refurb means broken an fixed and more likely to break again.

Probably 2 years.It would be unwise to buy a refurb one.