When I last looked at that line I thought there was still a fair amount of play in that position after 14.Qh4 (which John Emms discussed in 2000 in Play the Open Games as Black), but maybe it has been analysed in more depth sucking the life out of it, I don't know. I have sometimes played this 6.0-0 line myself with White but my opponents have never got as far as 9...Qd3, so I haven't really been tested in it. Black could consider 6...dxc3 heading for double-edged Göring Gambit positions after 7.Nxc3 d6 (7.e5 d5 8.exf6 dxc4 is also possible), which offer more winning chances for both sides, although it can be tricky to play as Black unless you really know what you're doing. 9...Qe7 instead of 9...Qd3 is another possibility, though I didn't really trust it when I last examined it.

I agree that there are more drawish options available for White. My main objection has tended to be 6.cxd4 Bb4+ 7.Bd2, where 7...Nxe4 8.Bxf7+ Kxf7 9.Qb3+ Kf8 10.Qxb4+ Qe7 is quite drawish and after 9...d5 White gets decent attacking chances in the lines where Black doesn't force an early queen trade. After 7...Bxd2+ 8.Nbxd2 d5 9.exd5 Nxd5 10.Qb3 Black must choose between allowing a draw with 10...Na5 or go relatively passive with 10...Nce7, which isn't bad, but I tend to prefer White in the resulting IQP positions.

I recently played in a team vote chess game on Chess.com with the Ulvestad line 5...b5 6.Bf1 where we allowed the transposition to the Fritz with 6...Nd4 7.c3 Nxd5 8.cxd4 Qxg5, and won quite convincingly, but White must have erred somewhere after move 8 because that line is known to be better for White with best play. I saw Levy Rozman (GothamChess) analyse the Magnus game with 6...Nxd5 7.Bxb5 Bb7 etc., which looked nice. Magnus should really have won it but missed an opportunity late on and Gukesh then found a number of accurate moves.

GM Ivan Cheparinov analyzes "The Best Opening Ideas of 2023"  at Modern-chess.com. He goes over 13 games. One is on the Ulvestad variation.

What is the point of the Two Knights variation? Nowdays, White will probably respond with 4d3 and the game will be a Giuoco Pianissimo. Why not play the simpler and safer 3...Bc4? Black can answer 4d3 with 4...Be7, but that does not attract me greatly. Cheparinov provides two games with 4...d5. Perhaps the Ulvestad and 4d3 d5 is a good response to the Italian game.

Modern-Chess is currently running a sale, 60% off. I assume they are offering a quantity discount of 10%, as they have in the past. Altogether that makes a 74% discount if you buy two or more products. Their prices are normally high, but this a good time to buy. Jonathan's book remains an everyday bargain by comparison.

Maybe!

Chess Assistant shows 15 games with the Ulvestad in 2024: 5 wins for White, 10 wins for Black, and no draws. The most recent game is from May 4th.