Forbidden Broadway's problems are not dissimilar to that of the York Theatre: the audience they're trying to cater to is too small to matter.
It's only relevant if you've seen a majority of the recent Bway shows, which means they can only advertise to frequent theatergoers. Within the ever-shrinking NYC-based theatergoing audience, there's not a Broadway monoculture. BTTF and Great Gatsby sell a lot of tickets, but I doubt the target audience for FB has actually seen them. As someone who sees a fair amount of theatre, why spend $40 on FB when I could see a new-to-me Broadway show for the same price?
F.B. has always been at its best when it's lampooning hit shows and successful performers. It also got some mileage out of anything that was "different" from the status quo of Broadway, but now diversity is being celebrated. There are plenty of things about Broadway that CAN and should be savagely roasted (shows, the business, and the people who inhabit it), but only like 75 of us would find it funny. When your show loses 19 million, you don't need some off-Broadway pipsqueak ragging on you. Not to mention the age of sensitivity we live in.
Musical theatre parody kind of peaked in the 2000s with The Producers, Spamalot, and Mormon, and more recently there's been Titanique, Big Gay Jamboree, Stranger Sings, etc.
Maybe it would be better as a series of TikTok sketches.