If you by new $250 isn't close to getting you anything decent which also works for streaming as far as I know.
Plus for many cameras you need to capture their video output, i.e. USB is not enough (through that currently changes). So you need a capture chip with low latency or else things are bad for "life" usage. This is often another 60-130€ for something decent if brought anew.
Plus they don't have a monitor clip so you need buy an additional stand.
Sure you can buy used parts but then you also need to compare it with used part prices for webcams which normally (i.e. non Covid19) are also lower.
I mean a Sony a5100 with usable objective currently sells new for ~US$700 but you can probably get it new for that price with capture card and stand if you buy clever and we ignore Covid19 for fairness.
(And even used you are still far above 250€ for any recent decently usable mirror less camera with objective in my experience.)
Plus for many cameras you need to capture their video output, i.e. USB is not enough (through that currently changes). So you need a capture chip with low latency or else things are bad for "life" usage. This is often another 60-130€ for something decent if brought anew.
Plus they don't have a monitor clip so you need buy an additional stand.
Sure you can buy used parts but then you also need to compare it with used part prices for webcams which normally (i.e. non Covid19) are also lower.
I mean a Sony a5100 with usable objective currently sells new for ~US$700 but you can probably get it new for that price with capture card and stand if you buy clever and we ignore Covid19 for fairness.
(And even used you are still far above 250€ for any recent decently usable mirror less camera with objective in my experience.)