not really infinite because of the phosphor elements being finite
There are other limitations, such as beam deflection imprecision and precision/speed of the A/D converter and the size of the electron beam in relation to it's brightness. Tighten the beam focus to get more precision, but it will be way dimmer and harder for a player to see. Make the beam stronger to compensate and you'll burn a hole in the phosphor. Your costs also go up with the fancier parts and beefier power supply.
The Atari system settled on 1024 points of resolution on each axis (but clipped to 1024x768 for the 4:3 monitors used at the time). Still a lot more resolution than the low-res arcade monitors of the day, which were roughly CGA-class (around 320x240).
Yup. There were some laser enthusiasts that connected their projection systems to MAME and created Laser MAME.
Laser galvo speed is a big factor in making it work effectively but there have been some great demos, like John Knoll (from ILM) playing Atari Star Wars on a theatre screen:
The limitation shifted elsewhere of course, and that's in the complexity of the scene, specifically the number of objects.
Still, interesting tech and can even be adapted to control a laser unit that renders on say a big building or even the clouds (the real ones).