There are plenty of roads between Middlesbrough and Thirsk that aren't the A19.
The A19/A168 is a road I've used plenty of times, both for transport and for TTing. There are other roads that go in broadly the right direction but it's still the fastest way of getting north/south on a bike if I need to get a move on.
The road between Thirsk and Middlesbrough has several TT courses: it's used at all distances, starting from both ends. There will frequently be two short events running on the same day, one from Yorkshire and one from Teesside. I've just tried to add up the number of times I've TT'd on there and I've literally lost count.
All that time, I've felt completely safe. I've never had a problem with being cut up, close passed or anything of that nature. There's never been a particularly large amount of traffic on there: I've ridden on many busier roads, both getting in and out of big cities and also when I've been touring and have needed to take a direct route.
Major trunk roads full of trucks and drivers with expectations of being able to drive at motorway speed unimpeded (yes, I know - that might not be right, but that's how it is) are no place for cyclists.
Why though? Do you think the cyclists are at risk because they are at danger of dying? In which case, referring to the A63, let's repeat:
The A63 is a safe road.
The cyclists on the A63 are not in danger.
You may think what they are doing is dangerous, but it isn't.
The road has been heavily used by time triallists for 20 or 30 years, hundreds of thousands of race miles, with a good safety record. The one single death was the rider's own fault.
Fear of danger is not a reason to ban cyclists from the A63.