It sounds silly to say now that Schwartz must be one of the wealthiest songwriters in Broadway history, but, despite many issues I do have with his work (usually to do with lyrics) I do feel that Schwartz never quite gets the credit he deserves. It's amazing to look back at early Wicked reviews that nearly all call the score completely generic and unmemorable. But then you realize that critics have ALWAYS initially said that about his work--Godspell, Pippin--especially-- Baker's Wife, Children of Eden, even many early film reviews of Prince of Egypt. Even minor works like Geppetto (hear me out--if it had been done by Dick van Dyke and Julie Andrews as the Blue Fairy I'm sure we'd appreciate the score a bit more) and his kid's musical Captain Louie... Sure, for example, Fosse's production of Pippin is largely responsible for turning it into a hit, but in hindsight, no matter what someone personally thinks of the score, there's no denying that it's the songs that have kept it around. I also thought that Queen of Versailles still shows he's in fine form even in his late 70s (and seeing his Viennese musical Shickaneder was honestly one of the best theatrical experiences and surprises I've had.)
Which is my long winded way of saying I think he deserves a tribute. I know he got one from the Met of all places last year (which you can hear on Youtube but I wish it had been filmed for PBS.) But, as others have said, it seems like it would be kind of out of place on the Tonys in their current state, especially with the only reason he'd get one right now being the Wicked film.
Wicked's success is interesting too because so many of its uber fans LOVE Wicked, but from what I can tell, it has not led to any interest in exploring what else Schwartz has written the way I think someone who falls in love with a Sondheim show might then check out his other works, or even someone falling for an ALW show (OK, there definitely are Phantom fanatics who, like Wicked fans, keep their obsession completely myopic and only on that one show...)