It sounds crazy because that isn't the whole story.
The F-35 comes in three variants, A for Air Force, B for Marines, and C for Navy. They are all variations on the same theme. The A is the base model. The B is pretty much the same as A but swaps out one of it's fuel tanks for a lift fan. The C is bigger version of A with folding wings, bigger wings are needed to have lower take off and landing speeds for carriers. Sharing a common platform save megabucks on all the radars, radios, FLIRs, fancy electronics, and the massive amount of software that needs to be written. It also gives them all a common engine, cockpit, and ejection system, which makes keeping spares on hand easier.
The F-35B replaces the Harrier because the Harrier is ancient and being better than it is a low bar to meet.
The F-35A replaces the F-16 by having stealth and a useful range. The F-16 was designed as a point defence fighter to defend against the Soviets over Germany, short range meant that it could be small, light, and manoeuvrable. Here are the typical combat ranges for the various fighters: F15C: 1,967 km, F-35A: 1,135 km, F-22: 760 km, F-18: 740 km, F-16: 550 km. The secret to the F-16's manoeuvrability is that they ditched a lot of fuel weight. The problem is the Soviet Union collapsed and the point defence mission disappeared. The F-16 found a new lease on life when the strapped an external fuel tank and targeting pod on it to give it enough range to be a bomb truck, but the extra weight of that fuel makes it shit for manoeuvrability. So the F-16 can either have range and shit manoeuvrability, or great manoeuvrability and a useless range. The F-35A has both, plus stealth, plus better infrared/optical sensors so it doesn't need a targeting pod.
The F-18A/C has the same problems as the F-16. So it is being replaced by two fighters, the F-18E/F Super Hornet for air superiority, and the F-35C for attack missions.
The A-10 is basically a plane without a mission. It was designed in the days before precision weapons when the only way to hit tanks was to strafe them WWII style. That means low and slow, which means it needed to be armoured against AA. Great, except the Soviets simply upped the AA from 23mm to 30mm, introduced their version of the Stinger called Igla, and added more armour to the roof of their tanks. By the late 80s the A-10 was a death trap, fly low and Soviet AA will kill it, fly medium and Igla will kill it, fly at normal hight and you can't aim. And even if you could aim it's questionable if the GAU could still disable most recent Soviet tanks. The final nail in the coffin is the Soviet Union collapsing. There are no hordes of tanks for the A-10 to kill so what good is it? Against even a moderate air defence network it can't survive, which is why it had to be pulled off attacks against Republican Guard in the Second Gulf War, too many were shot down. Against a unsophisticated enemy like an insurgency it is too expensive, if the enemy can't shoot you down send a drone. The done is more accurate, cheaper, longer loiter time, and can provide video feeds to ground commanders. During the wars in Afghanistan and Iraq the A-10 only provided something like 18% of the CAS missions, far less than the F-16s or F-18s. The USAF used the A-10s because they have them, but they don't want them.
The F-35 can replace all of those planes because one was hopelessly out dated. One had already lost its mission to the remaining two. The final two work okay, so the F-35 was designed as a upgraded version of them with better range, better sensors, and stealth.