There is a risk involved to violent engagement and I'm not familiar of examples of Saudi taking such risks in the past 60 years, but it's def. not my area.
While it is normal for vultures to attack a corpse, that is a very low risk engagement.
Think back to Gulf War 1 & 2. How much risk did Saudi take with Iraq? They allowed the USA to build a hyuge base to do their fighting for them.
I'm familiar with them putting down some Bahrainis around 2014 and the recent stuff with the Houthis and they are not impressive.
If they can pay or induce the Americans to do their fighting for them, that's what they're likely to do.
US is going to work with local armed groups, these have been cultivated for years already and they have much wider local support + a staging base in the direct rear (Pakistan, Iraqi Kurdistan) than any outsider will ever have. These local fighters will receive heavy CAS but for that to work you need American specialists embedded on the ground to properly communicate and navigate strikes. Likely highly trained SF teams will be working as well.
This move is yet premature though, US is still softening the military infrastructure in many regions and wearing down IRGC forces, ammo depots, command and control structures, etc. through relentless bombing campaigns. The problem: if these local groups, which are poorly trained and relatively small in number, fail to establish a foothold then the appetite for little nudge by US forces might increase and that's a slippery slope to actual boots on the ground, should not happen.
As for the Saudis, like all other high income and (relatively) cultured societies, they are casualty averse. This is somewhat of a problem, because the Saud Monarchs are ambitious in a number of fields, Empire building being one of them. In the first year in Yemen the 1000+ bodybags boundary was topped already, and constant Houthis incursions into Saudi territory became a national disgrace, aka advancing in reverse. Solving the problem of saving face and not losing their own people at this rate anymore was done the traditional Saudi way: by throwing money at it.
In this case that meant fat contracts for Western PMCs, and relatively decent contracts for the thirdworld rank and file. In the 2016-2020 timeframe the Saudis relied mostly on Sudanese, Colombians, Filipinos, Ugandans, Syrians and Pakistani, their cumulative numbers above 150k. Later, and other Gulf States did the same, the switch was made to Muslim Subcontinentals. Late last year the Sauds officialized this setup by signing a Defence Pact with Pakistan, this in reality means that Pakistan will fight for Saudi Arabia's interest and the Saudis will pay them big money to do so.
It's the same in other Gulf States. The Emirati forces are even worse, 80 percent foreigners whereas with the Saudis its mostly irregulars/ auxiliaries. In the Emirati forces foreigners mostly have the same national backgrounds as with the Saudis. In some recruiting countries signing military contracts with Gulf States as a soldier of fortune is now considered a top tier career move, it's a paycheck everybody desires. The Emiratis even copied the French Foreign Legion and started their own Emirati Foreign Legion