I have no idea what you think Saudia is trying to serve from BHX. Saudia is also targeting connecting traffic more than O&D traffic. A vast majority of the passengers using the Saudia route are not ending their journey in Saudi Arabia. I remember an article released a year or so after the launch suggesting that the vast majority of BHX-originating passengers were connecting onwards to India, Pakistan, and Thailand. And unlike Riyadh Air, Saudia already has the network up and running.
Riyadh Air is also positioning itself as a more premium airline, something that BHX's market has always struggled with more than its competitors.
In general, Saudi Arabia wants to grow its tourism network across the world, and it sees investing in its two main airlines as a way of doing that. You will also note that nearly all of Riyadh Air's announced routes are already served by Saudia; routes that the Saudi government knows work for them and wants to invest in.
In short, if Saudia doesn't think a BHX-JED route is viable with the connections already on offer, don't delude yourself into thinking that a more premium airline, Riyadh Air, controlled by the same people, the Saudi government, is going to jump in and save the day. That simply isn't going to happen.
Yes, Riyadh Air wants to compete with the likes of Emirates and Qatar and become a global player. That's a bold vision, but the airline is nowhere near that yet. Yes, I'm sure BHX is on their list for some point in the future, but if Saudia can't make it work from BHX, Riyadh Air will almost certainly see that as a problem, not an opportunity.