I think you overestimate the capacity of these hotels. The Embassy Suites might look big, for example, but I'll bet it has only about 150 rooms. The largest hotel in Buffalo, the former Hilton and Adams Mark, now called the Buffalo Grand, has 400.
My figures come from Visit Buffalo Niagara, which ought to know. https://www.wgrz.com/article/news/local/majority-of-buffalos-hotel-rooms-booked/71-ebd86012-b73a-4d58-8f69-ed768d206c03
And there are not a few thousand hotels in the area. Not even close.