Saudi Arabia cannot legitimize Israel, but Israel can delegitimize Saudi Arabia.
If Saudi Arabia normalizes with Israel hundreds of millions -if not each and every Muslim of the 2 billion total- will see it as a confirmation and validation of the Hadith that praises Yemen and the Levant but curses Najd.
Link to Hadith plus explanation in Arabic: https://www.islamweb.org/ar/fatwa/134719/
Rough Google Translation:
O Allah, bless us in our Levant and in our Yemen. They said: And in our Najd. He said: O Allah, bless us in our Levant and in our Yemen. They said: And in our Najd. He said: There are earthquakes and tribulations, and from there the horn of Satan will rise.
I personally don't think the Politico story is true. The risk is too damn high for the House of Saud. They will lose all legitimacy domestically and internationally.