If it can't loiter and it can't dogfight, then it can't cause your undefined "grief." So what are these fighters going to do, zoom up into the atmosphere, launch a couple of long-range missiles as they go by, then zoom back home? What will that do to stop Israeli (or American, for that matter) CAS? A little jamming, some chaff and flares, dive for the deck, and then when the rocket-fighters are zooming back home, go back to your mission. That's hardly air superiority.
Why don't you research the Me-262 and its use in WWII before you start fantasizing about your rocket planes. Sure, the P-51's couldn't catch them, but they flew fast and straight (one of the consequences of flying fast) and made very little impact on Allied Air. Other than attacking bombers, the Me-262 was completely ineffective in any role versus Allied CAP or CAS... just like your rocket-planes would be...
The ME-262 ran into the same problem as did the German Tiger II tank; it's hyper-expensive price made it too difficult to build enough of them to win against our overwhelming numbers.
...a problem which I'd prefer to avoid with our current over-budget F-22.