The *.mov file format is the same as MPEG-4's container format (in fact, MPEG-4's container is intentionally based on QuickTime's *.mov) and is even standardized as an ISO spec: "ISO/IEC base media file format":
https://en.wikipedia.org/wiki/ISO/IEC_base_media_file_format +
https://en.wikipedia.org/wiki/QuickTime_File_Format...and Apple has been using MPEG-4 AVC and HEVC for at least a decade now, so I don't understand what the OP is complaining about: QuickTime *.mov files are MPEG-4 container files, which usually contain MPEG-4 AVC or MPEG-4 HEVC streams.
Other people are reporting the same problem: the other media software can't read Apple's screen-recording files, so I'm assuming this actually means that Apple's screen-recordings are saved using a codec other than MPEG-4 AVC or HEVC, but still in an MPEG-4 container. So for this conversation to continue, we need to know what codec/video-stream-format is actually being used (I don't have a Mac ready to experiment right now, sorry).
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UPDATE: After some research, I think that macOS screen-recordings are made using Apple's ProRes video coding, and then saved inside a QuickTime (aka MPEG-4) Container.
ProRes is very different to AVC, HEVC, etc, which explains why you need to transcode it to do anything useful with it.
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UPDATE 2: So screen recordings don't use ProRes by default, they use AVC (but what profile?), so I'm unsure why so many other programs and websites reject those files because, theoretically, there should be no problem in processing them, unless the site was written by someone who doesn't understand how video files work...