Yes. In fact this Wikipedia article specifically gives the example of I-93 in New Hampshire.
I assume you are talking about Ohio Route 2, which for a section west of Cleveland (10 miles from my new place) shares signage with Interstate 90, then they diverge in Elyria and 90 goes south to merge with 80 (which is also the OH Turnpike). I believe one reason is that 2 west of Sandusky leading to Toledo is no longer a restricted-access highway, with normal stop-sign intersections representing the majority of interchanges.
The NYS parkways were not built with Federal funds and most predate the Interstate system. They are managed by the state of NY and various state authorities.
Once the Interstate system was set up, the New York parkway authorities had no reason to join it. None of the parkway system roads have route numbers, though some parkways outside of it do.
One reason why OH2 isn’t an Interstate is because the Ohio Turnpike is an Interstate. It was built to be a multi-lane, divided, controlled access highway, so it was easy to upgrade it to full Interstate standards and connect easily with the Pennsylvania Turnpike on the east and Indiana Toll Road on the west.
Another Ohio example is U.S. 30. While it’s four-lane, divided, and limited access along much of its path, it’s not all the way, and according to Wikipedia, multiple proposals to upgrade it across the state have been rejected.
Nah, the portions of the Shoreway that aren’t I-90 are an Ohio route, not a US route. That’s a clear difference, and if a state wants to build a really fancy road using state money with no federal involvement, there’s no reason they can’t.
According to your cite, not much of US 33 in Ohio is actually built to Interstate standards; in fact, a lot of it is still two-lane.
Another factor to consider is how much long-distance traffic the highway is carrying. I’ll bet most of the traffic on U.S. 33 isn’t going more than 50 miles, and not into either Indiana or West Virginia.
The NYS parkways also prohibit any commercial traffic, not just trucks. So someone’s Tesla that has their electrical company’s logo on the sides (and has NY Commercial license plates on it) is prohibited from using the parkway. Also you cannot take trailers onto the parkways.
Unless things have changed in NY, certain pickup trucks, even though used as private vehicles, still have to be tagged as commercial vehicles (due to size?) and cannot use the parkways. I personally miss Long Island parkways as I now live in Maryland and am forever stuck on major roads with every Tom, Dick & Harry small business vans and tractor trailers.