No, it's not untouchable. Any 4th gen fighter + with HOBS/AIM-9X and helmet mounted cuing sight would blow the F-35 out of the sky. It cannot turn, it cannot shoot, it cannot pitch or roll as fast as its competition. For crying out loud, the B variant and C variant are limited to under 7.5 G's in clean config. A F-16 with full load can do that. A clean F-16 can pull 9 G's fairly easily. The F-35A can do that, but it bleeds energy like no tomorrow.
Yes, the F-22 should have gotten helmet mounted cuing and AIM-9X sooner. Guess what, because of the money hole the F-35 is, the F-22 cannot get the funding it needs to obtain these quicker/at all.
We should have chosen the YF-23 to begin with.
A F-16 with AFTI canards, VISTA 3d thrust vectoring, and XL cranked arrow wing would have been a far superior setup to the F-35. Cheaper by an order of magnitude as welll.