I think it's easy to forget how incredibly simple and lucky all the mods we have for other gameboy models are.
Take the GBA for instance, the AGS-101 screen is really insanely convenient. The way I would assume the mod developed was someone noticing the pinout of the 32 pin AGB was almost exactly the same as the the pinout for the AGS-101 screen, I believe the only difference was that the pins were in the exact reverse order, and you had to solder power into one of the pins to power the backlight. (i don't have one handy, I THINK its reversed and not completely 1:1, but that's beside the point). From there, you look at the 40 pin AGB and notice, that while the pins are a little more scrambled, you can do the same thing by knowing the pin layout, some tracks have to be flip flopped, and that's why the 40 pin ribbons aren't all straight tracks, some are flip flopped here and there. Still, it's quite lucky that it just works, and it's incredibly easy to implement. It also makes for a very thin part that's very easy to fit into the case with the new screen. Really, we have the hardware similarity and of the agb and ags to thank, nintendo didn't fundamentally change the signals output by the display, they just developed a better display that could accept more or less the same connection pin for pin as the 32 pin AGB, and the 32 pin AGB wasn't a big change from the original 40 pin AGB.
If we lived in an alternate universe where nintendo just stuck to the AGB-001 for the entire run of the GBA, and never developed the AGS-101, we would be in EXACTLY the same position with the AGB as we are with the CGB-001. Front light kits would be the only choice.
One could imagine, and it's technically possible, that an LCD screen could be developed for the CGB in much the way it was for the AGS. That's where demand would become an issue though. I'm not quite sure what it would cost to develop a prototype screen from the ground up and make the first one, but the complexity and cost of that development is NOT trivial. I'll use like, the early models of Oculus Rift as a comparative example, they very much have piggy backed on already existing screens and with good reason. I'm like breaking into a cold sweat even thinking of mentioning it, and I hope I don't set anyone's mental disorder off by saying this, but regardless of how you feel about the facebook acquisition, one of the good items on the "pros vs cons" of that aquisition is that it's really at THAT point where phrases like "oh, money, now we can develop a purpose made screen that's exactly what we want" was even on the table.
Demand is another huge huge hurdle, like lets say you even have the exact manufacturing process and specifications nailed down, ready to go to the factory. Who is going to manufacture it? I have no idea what the minimum order size a plant in china would want to see, but I think they'd scoff at stopping to manufacuture 100,000 of a completely unique LCD. Say you did do, I seriously doubt that you could sell 100,000 of them profitably. The demand is not there. Reality check is that we're talking about a mod for diehard enthusiasts. Practically speaking, I don't see such a part ever being made unless there's some whacky star-trek-replicator-level technology somewhere in the future. It's completely non viable on so many levels trying to go at it the way products are currently manufactured.
Another somewhat exotic possibility would be a custom driver board for an already existing display. For examples of that kind of mod, look into current mods that exist for adapting modern LCD screens into a Sega Game Gear. They basically found a screen that they wanted to make work, then made a custom pcb that goes between that screen and the system itself, it's a video converter board. Said video board costs like in the neighborhood of $100 I think (don't quote me on that, I'm just going off memory, and it's hard to actually find pricing info publicly posted at all), and is made by some guy on I think atari age forums who goes by the name McWill. It's kind of crazy that he went to the trouble, but admirable. Some other similar Game Gear mods exist I think, but that's for you to research if you care to learn more, just using it as an example. The Game Gear does have an advantage when it comes to space to do that kind of crazyness though. The CGB is much much tighter. Does an LCD exist that is the exact size and resolution for the gameboy color? Of those potential screens is any of them thin enough to accomodate an entire PCB behind it? Doubtful, so you'd be looking to stuff the board elsewhere in the CGB and I kinda doubt it's physically possible to do, you'd be under really crazy spatial constraints, and in the end, you're going to probably be adapting to a screen that's just a little bit wrong aspect ratio or some other little picky detail like that, and you're just going to a ton of trouble for a result that's going to have the same kind of minor problems that the Kong Feng GB Boy Color thing mentioned above has.
So, sorry for writing a book, but that's my take on it. It's not like, against the laws of physics to have a CGB with a nice backlit LCD, but it's so unlikely to ever happen that I wouldn't hold my breath. It's not even that the work is just sitting there waiting to be done, it's like building a 7-11 on the moon for no real reason other than it would be cool. We can only be grateful that the AGS-101 came along and gave enthusiasts the option of playing the entire gameboy catalog on a nice first party, purpose built screen.