You're neglecting one of the most valuable roles for the A-10: close air support for ground troops in contact.
In that situation (read: the entirety of our conflict in Afghanistan/Iraq) tanks had NO ROLE. You're fighting a highly mobile ground force that often have an armament/position advantage and that's where the A-10 CAS really really makes a difference. Nobody fought TANKS in Afghanistan.
Ask anyone who's been in contact with the enemy how they feel when they hear that distinctive "BRRRRRRRAAAAAP!"
It's like FSCKING CHRISTMAS.
My father worked on A-10s in the Air Guard, I thought was very familiar with them... but it wasn't really until I saw that video that I realized how terrifying they are in the appropriate situation. While the above video is a friendly-fire close call, you're probably not going to find video like that from the other side of the line.
Having that pilot in that seat removes the need to replicate the kind of situational awareness you have when you're flying your plane 100-1000 feet off the ground and making passes to identify who is who so you avoid a friendly fire incident. Until we have the kind of immersive, low-latency, realtime kind of virtual reality you'd need, using drones for CAS is a pipe-dream.
Doing close air support you want A-10 pilots or Marines.
Even if the machine could not be retrofitted for carrier operations, the Corps could fly them from airfields ashore, and would really value an excellent ground-attack aircraft, and would take good extra-special care of them.
[1] in the Marine Corps Gazette I think.
Secondly, not every enemy has the latest tank. In fact, most potentially hostile nations (speaking from the POV of NATO) do NOT have modern tanks.
Because tanks only have that sort of armour on their frontal aspect and turret sides, and the top armour is very thin. Even if the turret top is armoured enough it is likely the engine deck can be penetrated and produce a mobility kill.
Also, hardly anyone besides the US and extremely close allies has ultra-modern tanks like late series Abrams or the Challenger II (and I have seen no evidence that those tanks are immune to the GAU-8).
P.S. There are also cheap ways to reduce shape charge effectiveness that don't work against solid penetrators. Things like the TUSK upgrade are designed to defeat RPGs not 30mm cannon.
That was a fairly long time ago, but unless armor has made huge progress since then, producing something hard enough to deflect this kind of force and yet light enough that the tank can move, I'd still bet on an A10 against anything rolling on the ground.
The top of a tank not so much and if you blow a track of that's a mobility kill - almost as good as a full brew up.