The median Fischer Random starting position is considerably more boring than normal chess. The minor pieces are often distant and the rooks and pawns get in the way of everything. This isn't just familiarity speaking; in real chess rook-and-pawn positions with inactive minor pieces are considered extremely boring.
Also, there is no such thing as a "solved problem" in the design of complex systems.
Not only at (very) high-level play, but also at normal time control. I seriously doubt if a typical player would play Chess 2 taking 1.5 hour for his first 40 moves, as professional chess players do... In speed chess there's obviously more mistakes, and thus considerably less draws, even among grandmasters.
Not clear, but I am wondering what that "a king crossing the middle line is a win" rule will do.
I have suspicion that that can lead to very early wins. "Move pawn, then rush king to fifth row" might be beatable, but I guess there are quite a few "recklessly run for row 5, and just make it" paths in the search tree. An easy way to counteract that may be bringing the queen and rooks into play early, but I would exchange them and then start the race for row 5.
Here's something that I think is in the spirit of the game and has a good chance of working:
Frame the game as two armies racing to occupy an oasis (four center squares of the board) in the desert. Consider that oasis occupied if either the enemy's king is captured, or if your king can camp there for X moves (if your king can camp there, the area can't be part of the front anymore, so it is truly yours)
I chose an oasis rather than a true stronghold such as a fort or castle because a fort or castle would have to mean the introduction of separate rules for attacks into and out of the stronghold (hm, that might be fun, too. Consider a case where captures into the four center squares require the capturer to have at least two means to make that capture.)
And draws are only very common at high-level play. It's not even clear this variant would solve that.