If the A-10 Warthogs are so useless to the USAF inventory, why are they being sent to Israel as an immediate action airplane?

For the same reasons they keep giving for trying to scrap the f14, 15, 16, 18 and now even talk of the f22. They have these representatives of the industrial military complex who keep pushing that the jsf is the only and therefore best replacement for all those planes. And when the planes they are trying to replace keep outperforming their supposed better counterparts they dangle in their faces, “but look they float and fly upwards, also here’s a contract for several billion dollars in your state. How about now?” This is the equivalent of saying that the b52 isn’t modern enough and then using them for 50 years to super great effect. The icbms in Montana are controlled by a floppy disc! And not a modern one, a literally floppy disc about a half foot wide. Why don’t they upgrade? Because they are unhackable. They are idiot proof, and they are reliable. As a mechanic I subscribe to : if it ain’t broke don’t fix it.

Not sure why the AF is always trying to get rid of the A-10. I suspect to the bean counters (in the AF) it really is a one mission aircraft. (not-Multi role)

Back when I was commissioned as an Armor type, the AF was trying to give the A-10 to the Army as its primary mission was to kill tanks (back then). I was saying Hell Ya, send it on over! But the powers that-be in the Army had to remind the AF of the agreement back in the mid 70's that the AF did not want us (the Army) flying guns on fixed wing aircraft. We had to un-arm all our Mohawks.

Because they are tough bastards; also they have tons of materials that can be salvaged and recycled

The A-10 Warthogs are an awesome aircraft! They are not called the tank killer for nothing! OOHRAH USMC!

I can spend all day discussing the advantages the A-10 has over the F-35 or F-22. One of the A-10's greatest assets is seldom discussed, its ability to keep flying while severely damaged and its ability to be repaired quickly. All the flight controls are easily repaired and can be swapped from the left to right side of the plane, including the main gears and engines. Then and all the backup systems to keep it flying, including two engines compared to one. Not only can the A-10 fly with severe damage, it has a fast turnaround to get back in the fight. The A-10 saves taxpayers money while doing the job it was designed to do, close air support within an area of air superiority. Bureaucrats have an issue with A-10's, its always been that way.

The A-10 is by far one of the most productive means of close air support for troops on the ground and I feel the brass want to spend funds like drunkards so they chose the warthog

Knowing Israel, their A-10s will be super up graded along with advanced tech. Coming soon the Israeli Super A-10.

Send them to the army, they will put pilots in them and make good use of them

It seems the premise of your question is flawed. The A-10 was a designed by pilots for the express purpose of close air ground support of the troops on the ground and for the Army pilots. There has been a lot of back and forth about who has them, the Army or the Air Force with the Air Force ultimately taken them into their inventory (after all who flies the friendly skies; certainly not the Army; such blasphemy be spoken). The Air Force in the philosophy of how to support ground troops wants an inventory of multi use aircraft and not one designed exclusively for one type of mission; close combat ground air support. This aircraft is so popular with combat ams soldiers that every time the AF tries to phase them out there is a hue and cry from the soldiers of such of magnitude that it reaches inside the beltway from the distant reaches of the world from Combat Arms soldiers which has made getting ride of them very unpopular no matter how the AF inside the beltway brass feels about the subject. They have thus been kept around longer than a lot of people have thought they would stay. It is a terrific addition to close combat and hopefully be kept around for many many more years.

Probably for the same reason the OV 10 Bronco was. Just too good at the job.