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.