I thought of this. Here's some catches:
Let's say you rip out a screen from.. I dunno... an old kindle fire. There's a small bundle of wires and a connector that fits onto the board. That wiring schematic for the screen is important... so you'll want to know what wire does what, i.e. red/white wire is red colors, green/white is green colors, green wire is ground, black wire is positive, white/brown might be data of some sort. There's going to be quite a few. And good luck finding a wiring schematic for some of these devices.
You might need an external power source. You MIGHT be able to power it off of USB. The wiring schematic should have power requirements.
Then you'll have to translate each of these wires to the RPi monitor cable equivalent. Some of the wires may or may not match up. Hack around a while... trial and error... If you got all this to work so far, then great. If not, then you might need an additional controller board.
Disclaimer: This is all speculation. I haven't tried this. I wouldn't mind trying it... I'd love to use an old dead laptop screen as an in-wall bathroom netflix device.
All this aside, buying the screen would be easier, but not as fun.