Is there a modern equivalent of that? Basically turn it into a thin client?

Well, X is still out there with its thin client capabilities intact. There are Wayland-compatible VNC clients and servers, if one isn’t big on X. SPICE is intended for connecting to VMs as servers. RDP if you want to use a Windows box as a server.

For a machine such as the OP describes, it would also be possible to install a tailored distro and software selection into the onboard space and place /home and such on a network drive, although that makes it impossible to take the tablet out of range of the LAN. If the touchscreen doesn’t work under either the Wacom or libinput drivers, it would probably be a waste of time, though.

(Really, 16GB is plenty for the distro itself—if I remove the three kernel source trees, a couple of games, and some FreePascal stuff, my desktop system minus /home would fit in that, and it’s anything but minimalistic.)

Yeah, that’s how I was taught in school in Canada in the 1980s, although no one ever explained why. It always did seem odd.