The cheapest flight I can find from Punta Cana, Dominican Republic to Raleigh, North Carolina, has a 15-hour layover in Charlotte, NC. I would much rather just rent a car in Charlotte and drive home, than wait for the next flight to Raleigh. When I arrive in Charlotte and go through customs, can I not recheck my bags and just end the trip in Charlotte?
I've never come through Customs at CLT, but at every other airport, you can just collect your bags and walk out of the customs hall no problem. No one will inspect the bags and force you to recheck them.
To be clear, you are violating ticketing rules and contract with the airline, but this is otherwise a common practice.
As a side note, 15 hours is a long time and it's possible they might not accept bags so far in advance, especially if it's overnight, even if you wanted to re-check. I checked, aa.com presumably, and see the 4 hour rule for certain stations. CLT is not listed.
You don't have to recheck your bags. Once you collect them and pass immigration, you are effectively "landed" in the US.
I would collect the bags, go to the rental place, collect my car and be on my way. 15 hours is a ridiculous layover time.