Another reason to not use a DSLR is that many (all?) have timeouts (<30min) in their video mode due to some import tax reason, even when hooked up to a computer.
Atleast this is what I found when I tried a canon DSLR with canons webcam software.
That's only if you actually hit the record button and are actively recording to the memory card, but if you're using the DSLR as a passthrough, it works all day. I have done it w/ my Sony a6500 and it works really well.
Sony cameras work (as mentioned below) but nearly every mirrorless or dslr I’ve used does this by default or can be set up to by switching to continuous AF modes. This is best done while connected to a power source, as the motors drain battery faster.
This changed in 2019 IIRC. The EU changed its regulation and the 30 minute record limit no longer applies. Furthermore, it was always possible to install custom firmware on many cameras that bypassed this limit. Record limits due to temperature and overheating, though, is a different story.
"Digital cameras that are only capable of recording still images remain classified in this subheading. Cameras of this subheading may also have video-capture capability to record continuous periods of video. However, when such apparatus are capable, using the maximum storage capacity, of capturing video in a quality of 800 x 600 pixels (or higher) at 23 frames per second (or higher) for a continuous period of at least 30 minutes (regardless of the fact that the captured video images may be recorded in separate files of a duration of less than 30 minutes) they are always to be classified in subheadings 8525 80 91 or 8525 80 99."
Is it such a big issue? My Canon DSLR turns off every 30min, but that's only for a couple of seconds, it then turns back on. On a positive side, it's now easy to notice when 30min or 1hr meeting is running over, it's a nice reminder :)