One example for you, Hogan (actually the only relatively recent one I can think of): Sons of the Prophet. Robyn Goodman had the money all lined up for a Broadway transfer after it's run at the Pels but the only theater available was the Broadhurst. They were in contention for the Lyceum but the Shuberts opted to give it to Venus in Fur.
Other than that, I do agree with your general assertion that theater availability is rarely the ONLY reason a "worthy" show doesn't make it to Broadway.