There has been a related question in the past but it is from over a decade back when smartphones were only beginning to get popular and mobile UI/UX wasn't as well established and most devices were much smaller than today.
Often on a mobile device when I start playing the video in inline mode, the details are not very clearly visible. And the experience is too distracting because there is a lot of other content around. So it is difficult to decide whether the content might be interesting to watch further.
Does it make sense to by default play videos in full screen mode with an easy way to exit the full screen video?
Yes, it makes sense. I'm going to be contrarian here and say that apps should optimize for the overwhelmingly primary task that users want to perform. If most YouTube users are playing the video and then tapping the screen to expand the video to fill the horizontal viewport, that in theory should become the default. Playing a video back in a tiny section of a vertical screen is usually suboptimal UX.
But there are a number of valid reasons not to do this:
They might have data that most users are stopping the video after a few seconds and going somewhere else; i.e., filling the video to full size is not the usual action taken after starting to play
Making users hold their device a certain way is an accessibility problem, because not all users can turn their devices. Sometimes the device is mounted to something that doesn't turn. Sometimes the user can't turn their wrist.
It is good to question why things are the way they are, though. There was a time when http was the default protocol and suggesting that all websites should use https was a radical idea. Your favorite sites and apps looked a lot different before their owners started testing assumptions. Be the kind of UX person that challenges why things are the way they are.
It is not the standard and I don't think it should be
The standard seems to be
Page with small thumbnail of video
User clicks thumbnail -> Video starts playing in small frame
User clicks expand button in video -> Video expands to fullscreen
I have not seen it any other way. And I think it would be distracting to play the video in fullscreen in the second step.
Here are some reasons:
User might just want to start the video to hear the audio (and browse the rest of the content, e.g. comments)
User has not decided if the video is any good. In the beginning the user wants to know if the video is good in terms of content and quality. If the audio is bad or the video is full of ads, a user would most likely end the video (not requiring fullscreen).
Fullscreen playing the video requires the user to rotate the phone to landscape view. Users don't like to be forced to rotate their phone.
I would suggest letting the user manually tap the video with an icon to play because the user may not be ready to watch it at that point and there might be other details they may want to read before watching it.
I think it is safer to NOT start in full screen mode by default if you are in portrait mode. First of all, try to keep the default dimensions each operation system uses (ios and android, they are somewhere half the screen in portrait mode). This is because, mobile users need more "usability" than desktop users. Maybe there are some important features of the app down from the video section (like youtube app, for example with other video thumbnails or comments, etc...). And it will be very frustrating for them to tap for exit full screen and then tap for pause video and then scroll down... But if you keep it not full screen by default then they dont need many taps! Also, i suggest to make the video full screen when the user uses his/her mobile phone in landscape mode.