Why does the government care what the other hospitals think? Would they stop a new burger bar opening too close to a McDonalds, if McDonalds petitioned them for long enough?
Yes, it's the way the world works. Homeowners vote against new developments (which decreases the cost of their homes). Everyone with a liquor license lobbies against more liquor licenses. Every grocery store lobbies against more grocery stores. Amusingly this causes big issues between state governments (who wants growth) and cities where most voters/business owners want to limit growth to protect themselves.
The cynical reason is because the hospitals are massive tax-bases and the owners of the hospitals are political donors.
The other reason is that the government has an interest in maximizing economic growth, among other things, which is why it has zoning power. Citizens in the area, including local businesses such as other hospitals, may raise any number of concerns about building projects. Further, any citizen (or corporation) can hold up just about any project for as long as it's willing to keep paying legal fees to fight projects based on trumped up bullshit about esoteric zoning laws that were written a century ago that they probably broke when building their own hospital.