I didn’t run into this problem, I started running mythics as soon as I qualified and no one really got in my way. The best way to handle this is to run your own key, then you get to go regardless. You choose the group, etc.
I also did this when people wouldn’t PUG me for Narathia, I just Raid Led my own group without having any idea what I was doing. I didn’t get to the end, but I got to experience some content and it was a good learning experience.
I guess when I think about it, my response to any kind of gatekeeping is always to become the one who is the gatekeeper. There is always tons of people desperate to get into content, and you get plenty of applications.
I kind of have this attitude for everything in life. People were no longer writing the kinds of books I wanted to read, so I just started writing books.
I did some mythic dungeons when they were added. Understood at once what they would become, and never ran mythics again. Doing dungeons a couple times on heroic is more than enough for me.