In the US, a vehicle with an outstanding recall technically isn't roadworthy, though consumer level enforcement of this is non-existent in practice. It's mostly enforced on dealers, who can't sell a vehicle with active recalls. The only way I can imagine it mattering to a consumer is if they sold it.
I can imagine car insurance refusing to pay out in the case of an accident
Doesn't being legally non roadworthy only apply to NHTSA safety recalls while there are other types of recalls for non compliance or manufacturer voluntary recalls?
Having worked (on the vehicle registration system) for a state agency that is a combination "department of motor vehicles" plus "highway department", there could be a case made that since your vehicle does not meet NTSB/DOT standards, that it isn't roadworthy and the best you could get would be a SALVAGE title. Which would require expensive inspections if you try to sell it or register it.
In Europe, car manufacturers have to show that their cars meet safety standards. In the US, car manufacturers only have to say/certify that their cars meet safety standards. This is the huge sticking point for Trump's attempt to force EU countries to accept cars that have not been proved to meet safety standards (it is portrayed as "unfair/uneven trade barriers" in the US media).