I see some false equivalence here. You've talked about national teams beating each other, whereas I think Saudis national team is already stronger than their league.
By that, it's recognised as being fairly decent - especially in the region. But, they want to build the profile of their league to become a global player.
And to do that, you need to attract global talent to play there. Look at the PL for example, it is recognised for having top talent, but what percentage are English?
La Liga has top Spanish players, but it's also known for attracting the best South American talent, alongside big players from Europe and elsewhere.
So do to that, you need to attract players from elsewhere, which in turn will attract audiences from around the global. There, they hope, it'll become cyclical.
In terms of grassroots, I've said the same (see below), but it isn't going to be a quick fix. Developing the league through foreign exposure may help that.
It'll only go to strengthen their national team, like you referred to, but as I said that ain't their primary goal. That's to make their league the pinnacle.
How many are Saudi golfers are there? That hasn't stopped them spending billions on LIV golf, to make it the most prestigious tournament. Their tournament.