1. You don't list the carrier or the routing.
2. The only domestic USA carrier I can think of which does this is DL at NYC between JFK & LGA. Depending on factors nobody can qutie figure our, you get a bus, taxi or car service voucher.
3. Luggage, if any, is your responsibility, even if it's DL at NYC. You pick it up at JFK and schlep it to LGA where you check it back in.
4. Risk of misconnect is pax. Flat tire rule may help, but there are a lot of people who've tried to save money with this and wound up spending a minor fortune on hotels & meals.
5. Even on reroutes many carriers won't provide local transport unless the reroute was avoidable (MX). Travel interruption insurance a must if you're not in a position to absorb costs of delay.