Well, it is obvious that a Wizard is stronger than a Queen, because it is upward compatible. The question is how much stronger. That it draws against a single Queen, and loses against two Queens when the Kings have enough of a Pawn shield to protect them from a perpetual, doesn't suggest an insanely high end-game value, though. In the middle game it would obviously have a huge advantage compared to normal sliders, which lose a lot of mobility on densely populated boards. It would be very interesting to see how it functions there. It is not a piece that I could configure Fairy-Max for, though. It would require a program modification to do that. And perhaps the KingSlayer engine would be more suited for such a modification.
Chess Variant Creator, if you have questions.

I don't think you can compare pieces in an endgame for their value. It looks like with this piece you would checkmate in the late opening or early mid-game. That's where you would need to focus your valuation. If you want to know how much I'd give up for a Wizard, I would give up a Queen (to replace), two Rooks, and a Knight. I think I could comfortably compete against a standard set. That's 9+5+5+3= 22 points.
What would you feel comfortable giving up?
Well, that is not nearly 30. And it might already be too much. I suppose I would prefer having a Rook + 4 minors over a Wizard. Not much he can do, with just one Wizard and one Rook. Even 4 minors might be enough, then he only has a Wizard and two Rooks. But strong pieces of course always do poorly against large number of weaker ones, remember the 3Q vs 7N case. So this might not give a good estimate for the value. It should really be play tested to be sure.

So this might not give a good estimate for the value. It should really be play tested to be sure.
Agreed.
There really exist variants with pieces that are that valuable, or even more. But they are usually a lot bigger that Chess. Tenjiku Shogi (a game on a 16x16 board, with 78 pieces per player) has a piece called Fire Demon, which is easily worth 8 Queens. And you start with two of those. It is so valuable, not because of its move (which in itself would make it more valuable than a Queen), but because it doesn't only capture what it lands on, but also 'burns' all adjacent enemy pieces. (A bit similar to Atomic Chess, except that it doesn't destroy itself in the process, but can do it every move.)

Regardless of the value of the Wizard (we all agree it would be valued higher than any known piece), this variant would be about that one piece first because losing it would be like losing the game. It's omnipresence would have to be considered for any attack or defense. You might just change the name to "The Wizard".



It would certainly be a very dominant piece, and as Queen replacement in a FIDE army it would probably not work very well. (Similar to the Amazon. One problem is that when the Rook is the next-highest piece, there really is nothing you could trade it for other than the opponent Wizard. In FIDE you can at least still do Q for 2R or Q for R+B without being completely lost.)
In Chu Shogi the strongest piece is a Lion, worth about 60% more than a Queen. But Chu Shogi is a large game (12x12, 46 pieces each), and there also is a Queen, and 4 pieces that can promote to a nearly Queen, in addition to pieces valued between Q and R. So there is plenty of opportunity to do near-equal 2-for-1 trades with a Lion there.
I am not sure how much the other pieces are worth in the mentioned game, though. They could be worth more than a Rook.

True, but as I mentioned, I am not sure that the Archers and Tanks are stronger than a Rook. (And even if so, whether they are very much stronger.) And the Long Knight is definitely weaker than an orthodox Knight.
So there doesn't seem much possibility to trade a Wizard for other material.

My point wasn't that in this specific scenario it was going to happen, just that it's something the Wizard is insanely good at and that a regular Queen will not be.