As others have said its a combo of issues but primarily its because you have to roam so much to ward that you lose lane xp compared to the others. As you have noticed the inspiration mastery does nothing to really help.
Riot makes no sense when it comes to how they deal with supports. Its clear at this point what the support role generally does and is responsible for and yet Riot still chose to tie support gold income to items that require you to be in lane to get the maximum effect from them. So to be a good support you have hamstring yourself XP and gold wise. Pretty sure Riot has said those sorts of decisions being forced on players is a sign of bad design, but hey its supports who are getting shafted, so Riot cant be bothered.
There is no good reason supports should suffer inequities on the level/xp front, but 5 years in, there supports are, still getting shafted. The saddest part is clearly Riot knows supports suffer from this hence the inclusion of the inspiration mastery. However that is all that mastery accomplishes. It lets us know Riot sees the issue and yet has no clue how to solve it apparently.
Riot has been pretty consistent in showing though that they see all the other roles and their needs as more important than the support roles (see the long list support champ nerfs the moment they step into some other lane or the long list of support itemization nerfs as soon as support items impact some other lane). Dont expect any fixes that actually work. That would require effort which Riot would rather put toward all the other roles they value more highly.