Eek, the thought of that makes me cringe. I guess it would be passable in some circumstances, but I can imagine a bunch of reasons why it would be miserable or useless:
* the quality drop; recompressing, non-matching frame rates, non-matching resolution--all the same goes for audio. You're very likely clipping (losing) data. This is assuming you're doing screen-capture. If you're literally video taping a monitor you will get moiré in the video, room tone in the audio, losing any stereo separation, and other audio/video artifacts.
* performance; must be done in real-time, cannot queue up multiple sources. This is likely the biggest efficiency killer and makes things 100x more labor intensive.
* reliable Internet; if you get a blip or have a slow connection you have to hopefully catch it and start over. With youtube-dl you can pause, resume, confirm even on the slowest, spottiest connections.
* metadata, organizing, indexing; likely hand-typed separately, prone to error, prone to not knowing if you've done that video already.
* Chain of custody; grabbing the original video allows you to prove two identical copies match (using file hashes or other comparisons) screen recording makes that difficult to impossible to confirm--maybe with fancy AI you'd have to run by the courts?