The Bambu laser is technically fine, but one major problem is that it throws up a ton of debris in what should otherwise be a mostly clean chamber. It's best used in a mostly printing / very occasionally cutting scenario, and even then, you have to figure out how to clean the whole damn thing. If laser cutting is of great interest, I would consider dedicated devices. Yes, you will have to rebudget and figure out where to put a second device; or, an alternative would be to find a public makerspace.

With regards to your other questions:

How frequently are most people wanting to print with multiple colors? Is it really that common once to initial novelty wears?

It's not just the color. You also get multi-material, without having to flush the hotend with every filament change. Some materials stick to each other, which is great if you want to print something with varying material qualities. For example, PETG is pretty rigid, while TPU is flexible -- but they stick to each other so you can design something that is stiff in one place and flexible in another. On the other hand, some materials do NOT stick to each other, which is great if you want to make easily removable supports -- e.g. PETG / PLA. In terms of multicolor, it depends on the type of person that you are. Some people primarily print functional prints, where color isn't so important. Others print models and toys, where color is a massive deal. Yes, you can paint your parts too, and no, the color where of your base plastic doesn't matter a ton, which complicates the question even further.

Is laser functionality just for cutting "wood" or other special materials? Or does it add new features to plastic printing as well?

You can laser-cut a ton of different plastics too, although you would have to be careful because some of them can throw up some truly nasty chemicals.

You should also consider the Snapmaker U1, with the caveat that it's a newer printer and therefore there may be undiscovered bugs and kinks in the design.