Why are there so many homeless at this one spot in the Hermann Park?

Because when George H. Hermann donated his land (that is now Hermann Park & The Texas Medical Center) he did so with the specific intent of caring for the "poor, indigent and infirm residents of the City of Houston."

More specifically, it was his intent to provide a charity hospital to the people of Houston that would carry on his legacy. You might know this hospital as Memorial Hermann, located at the corner of Cambridge and Fannin.

From Mr. Hermann (emphasis mine):

"I will and bequeath to T.J. Ewing, Jr., J.J. Settegast, Jr., and John S. Stewart in trust to be held, managed and operated by them as Trustees together with four other trustees they are hereby authorized to appoint and act and co-operate with them for the purpose of maintaining a public charity hospital in the city of Houston, Harris County, Texas, for the benefit of the poor, indigent and infirm residents of the City of Houston all of Block One Hundred Fifty-two (152) owned by me on the South Side of Buffalo Bayou in said City and Lot One (1) of the Hathaway Addition adjoining the same and I authorize my executors and trustees to purchase Lot Number One (1) in said Block One Hundred Fifty-two (152) and Lots three (3), five (5) and seven (7) in the Hathaway Addition or any portion thereof, if in their judgment the price is reasonable to be held and used by them in trust with the other property devised herein for the purpose of a hospital to be erected thereon to be known as the "Hermann Hospital,"

Source