It's not really equivalent to forum posts in that particular location. It's just a tooltip. The default list (and the potential list seeing as many admins add additional ones) is far too big to fit reasonably within a tooltip.
This is equivalent to the forum posts UI, and it does list them:
Yes, but as a mere tooltip, what's wrong with the list. If it needs the list on a post, it needs it with Media Gallery. If it really is too big for a tooltip, then a link to the media site list on the becomes page would be at leat informative.
You're comparing apples to oranges. When posting on the forum there is no equivalent "Allowed types" list from the screenshot in your first post. The list you're talking about is shown in an equivalent place when adding media.
The process of embedding a media site URL in the gallery and embedding a media site URL in a forum post is nearly identical.
To embed a media site URL in a forum post, you have to click the Insert > Media button and then you get this overlay:
To embed a media site URL in a forum post, you have to click the "Embed media" button and then you get this overlay:
So there's no inconsistency here, the process and UI is identical.