Former mortgage broker here. This is basically a credit union, or a private lender.
Now I'll explain why those exist, but your idea doesn't exist.
Repayments are paid the $200 in return in a random time frame of between the first month to the last month 30 years later.
Every year that $200 loses 2.2% of it's value. So you have to charge interest or else people would be signing up to lose money (buying power).
But that creates a new problem, who gets paid when?
Assuming 5.5% interest (low end of rates right now) and a 25 year amortization, the people who got paid out at year 1 would receive $207 while the people paid out at year 25 would get $788(~$450 of buying power though).
Than there's the aspect of insurance. Your mandatory mortgage insurance covers the bank, not you. So now you need to find an insurer that can work with up to 2500 beneficiaries.
Or how bout when the bank forecloses for non payment?
It gets messy really fast and I'm just scratching the surface.