You'd be hard pressed to find more than a few people who do know that. As far as most people are concerned, it's a football stadium that's grudgingly opened up to other activities.
A separate national stadium for RL would either be a massive white elephant of a stadium that's little more than a money drain or an inadequate venue that's little, if any, better than what we have now in the club grounds. Surely it would have to be the ground for finals as well as internationals therefore would need to take 30k as an absolute, scraped minimum and realistically 40k to make it a viable option, then you have to consider it's fitness for other sports, concerts, etc. to lease. It's worth remembering that unless the stadium at least pays for itself then funding for it needs to come from somewhere. A good comparison would be the Welsh RU who still painfully struggle to keep up with the bills on their massive stadium despite filling it at least 3-4 times a year with RU internationals with the inevitable knock-on effects on sport-wide funding.
Then there's location. It really has to be up north somewhere, putting it near London does two things: first makes it difficult for the bulk of RL people to get to and makes the land prices, planning and build costs idiotically high. There's no point having a national stadium for a sport if its location gives people another excuse to not attend international games.
I'm strongly in favour of keeping leasing big grounds with the occasional trip to Wembley. We need to be realistic in that we can't afford to build and own a big, top-end stadium, we get the benefits of that by leasing a ground with none of the pitfalls of having to actually own one.
But, again, the issue is more - what exactly are we tied into with Wembley and what does it cost? It is our stadium even if no one knows that.
If we have to put two games there each year, which is my memory of the arrangement, then it makes a national stadium along anything other than Jonty's award-winning suggestion a bit pointless.