Why searches like youtube work very differently/bad on mobile devices?

When you upload a video to You-tube, you have to explicitly allow it to be played on mobile devices(I'm not sure what the default state is); so if a video cannot be played on mobiles then it does not show up in the search AFAIK.

Since it is mainly producers and official videos that do not show up, my first guess would be maybe allowing playback on mobiles used to reduce Ad-revenue. I remember a while back certain devices could not display ads during videos.

Search results are personalized so make sure you are logged in on the same account on the phone and the computer. Also, many videos are marked as "not viewable on phone" by their uploaders, so you can't watch them on the phone, and hence they won't appear in search results.