Inkjet as a technology doesn’t stand up well to intermittent use due to ink drying out. I think a lot of consumers buy a printer and use it rarely (idle for weeks at a time). In my experience using an inkjet this way leads to dry ink clogging the head. People don’t easily forget technology letting them down when they needed it.

Does this still happen with current printers or is it one of those ancient memes about printers which don't disappear?

When I turn the Epson one off, it audibly parks the head. I would suppose it is parked onto a gasket which would prevent it from drying out.

Personally, I don't buy laser printers because I cannot imagine that toner dust isn't unhealthy, and I would be scared of it leaking into the air I breathe.

Feel free to prove me wrong with studies, I would appreciate being less scared about it for my next printer in case the Epson does die some day.

I expect it doesn’t matter if you only print occasionally, but toner exposure from operating printers seems to be a significant health risk: https://pubmed.ncbi.nlm.nih.gov/29233006/

It very well could be a problem that has been solved. I have never owned an inkjet personally because of how much trouble my dad had with them when I was a child. I have owned the same laser printer (an HP i found at a second hand computer shop) for the last ten years, and it has basically just worked. I’m just nearing the end of the first tonor cartridge i bought for it, I print relatively rarely, but so far it has just worked every time.

Ecotank ink is water-based and more dilute than the normal stuff, apparently to reduce the liklihood of clogging. It needs a cleaning cycle every few months - that's it.