Let's concede that the head-on-cartridge design is to be praised, even if it increases the cost of the cartridges.
Head-on-cartridge was one of the reasons I ultimately ditched Epson for HP. The HP carts at the time had the print head built into the cartridge, so if I ran into problems, I simply bought a new print cartridge and life was good.
Epsons have the print head built captively into the carriage, which makes cleaning the print head all but impossible unless you work for Epson.
I eventually switched away from HP after I ran into a problem with my HP color printer of many years. It seems that even keeping the print head on the cartridge doesn't eliminate all problems. I thought my HP had some kind of print head clog from me not printing in color for a while, but that wasn't it. Turns out it was a logic problem in the printer.
My solution was to buy a Canon. Canon keeps the print head separate from the ink tanks, and each ink color is in its own tank. I purchased one of the 6-color photo printers which had special photo-cyan and photo-magenta colors in addition to the usual CMYK. What sets Canon apart from Epson, though, is that the print head can be removed from the unit and replaced without any special tools. You install the print head when you unbox the unit and set it up, and only ever remove it if there's a problem -- the only downside to this is, by the time you need to replace the print head, it might be impossible to find.
So in conclusion, I would say that head-on-cartridge is good (especially for low volume printing where quality isn't paramount), but having a user replaceable print head is the best possible solution.