Hi Aaron-
I manage a few properties with HCVP tenants, and it can be a mixed bag, for sure. Yes, you can generally get rents above what you'd get on the market otherwise, and it's nice to have the safety of the government backing up your payments. There's also a very ready pool of potential tenants, especially once you build relationships with DCHA and case workers.
BUT, there are also some major pitfalls. Depending on how you're screening your tenants, you may have a hard time being able to find someone suitable if you care about credit scores and rental history. Many have previous evictions, lots of collection accounts, etc. My experience has generally been that our voucher tenants don't have much experience in how to take care of a home, and put in a serious amount of maintenance requests for things as simple as changing lightbulbs. Also, if you're not familiar with the amount of paperwork required to lease up tenants through voucher programs, it can be a bit daunting the first few times.
As for your second concern, this is also a very real thing to worry about. Less so with traditional vouchers, (as my experience has been that people receiving them can often get extensions as long as they follow the rules of the program) but definitely so with rapid rehousing vouchers. These only last for a year, and we've had several problems involving tenants who simply stop paying once it expires and force us to evict them. When you consider the time and expense in getting them out, suddenly that extra money you were making per month in rent evaporates very quickly.
Bottom line, it all comes down to finding the right tenant. A quiet, respectful tenant who treats your property well makes the HCVP program extremely rewarding. But there are some nightmares out there, so use caution.