* transmissivity of an LCD panel is pretty bad (10%-25% transmissivity?). So this is always going to be extremely dim, unless you stick a really bright lamp right up close to it. Thus, this isn't "matching" ambient light in any way.
* Brightness uniformity is going to be terrible unless you use a photography softbox lamp.
* Color accuracy is going to be terrible. Monitors use LEDs that are extremely cold / blue (~6500K if I remember) to get good color reproduction over the entire range of possible colors. Unless you want your house to look like an operating room you probably won't use a lamp that comes close to reproducing that.
This is a solved problem in cellphones. Put a $0.25 ALS in the front bezel, enable DDC/CI, and call it a day.
Here's a product idea that actually solves the issue: make a little USB dongle that has an ALS in it, make it in a formfactor that allows you to clip it to the top of any monitor, and use that to control the brightness. For DDC/CI monitors, you can directly control the backlight, and for other monitors you can just fake it by reducing the brightness of the image.