In truth the ones I was designing a couple years ago were that method. Tiny and TS300 both have a fixed bed with print head moving through X/Y/Z.
I haven't seen many systems that do that style due to the z-axis generally making the X/Y less rigid or more complex. I was following that design because I wanted to go into other technologies, some of which included things like liquid baths. Leveling a four-screw design is quite challenging but once it's leveled and everything's set you shouldn't need to do that again.
If the z-axis in a printer is good and solid, it doesn't matter as much about the bed being fixed or moving through Z. The Z-axis is the slowest and least moved axis.
Regards,
Loial