In a bright room, the contrast was typically lacking.

Even on relatively late versions like the Toshiba 57HX93 (a 57" 16x9 doghouse from ~20 years ago with an integrated scaler and a 1080i input), which I personally spent some time with both in Toshiba form and as $10k Runco-branded units. Things got washed out in a bright room compared to a direct-view CRT.

And viewing angle is an issue, too: Whether front- or rear-projection, one of the tricks to improve brightness (and therefore potential contrast) is to reduce the angle of light transmission from the screen. Depending on the room layout, this can mean that people in seats off to the side might get a substantially darker image than those near the middle. (This applies to all projectors; film, CRT, DLP, LCD, front, rear, whatever -- there can be a lot of non-obvious tech that goes into a projection screen.)

And CRT projectors were fickle. Their color convergence would change based on external magnetic fields (including that produced by the Earth itself), so they needed to be set up properly in-situ. A projection set that was set up properly while facing East would be a different thing when rotated 90 degrees to instead face North: What once was carefully-adjusted to produce 3 overlapping images that summed to be pure white lines would be a weird mix of red, blue, and green lines that only sometimes overlapped.

The CRT tubes themselves were generally quite impressively small for the size of the image that they'd ultimately produce. This meant pushing the phosphor coatings quite hard, which translated into an increased opportunity for permanent image retention ("screen burn") from things like CNN logos and video game scores.

Plus: They'd tend to get blurry over time. Because they were being pushed hard, the CRTs were liquid-cooled using glycol that was supposed to be optically-clear. But stuff would sometimes grow in there. It was never clear whether this was flora or [micro]fauna or something else, but whatever it was liked living in a world filled with hot, brightly-lit glycol. Service shops could correct this by changing the fluid, but that's an expense and inconvenience that direct-view CRTs didn't have.

And they were ungainly things in other ways. Sure, they tended to be lighter (less-massive) because they were full of air instead of leaded glass, but a rear-projection set was generally a big floor-standing thing that still had plenty of gravity. Meanwhile, a front-projection rig ~doubled the chance of someone walking by occluding the view and came with the burden of a hard-to-clean screen (less important these days, but it used to be common for folks to smoke indoors) and its own additional alignment variables (and lens selection, and dust issues, and, and).

So a person could deal with all that, or -- you know -- just get a regular direct-view CRT.

Even today where projectors use friggin' laser beams for illumination and produce enormous, bright images with far fewer issues than I listed above, direct-view tech (like the flat LCD and *LED sets at any big-box) is still much more popular.

(But I do feel your pain. When I was a teenager, my parents came home from shopping one wintry night with a 36" Sony WEGA for me to help unload. Holy hell.)

Projection TVs were even prone to CRT "raster burn", perhaps even more so than single-tube TVs due to the brightness of the image required, which is why Nintendo instruction booklets had stern warnings not to use their consoles with projection TVs.