I am fine with a ball that sails out of the end zone being flagged an "illegal kick".
But then give the receiving team the option:
a) Field the ball at the "x" yard line (5? 10? 25?) OR
b) decline the penalty, give up a point, and field from the 35
I don't think this changes the mentality of the kicking team. If going for a field goal, they go for a field goal, they're not going to ALSO make sure they have the option of a point on a missed FG.
If they are trying to "punt for a single", well, then it just got a bit tougher, and I think that's fine.
The receiving team will still put someone back to field the ball, because it would be silly not to.
While this does give extra leverage to the receiving team, it is similar to what happens if the kicking team hits the upright. Hey, maybe we should allow the receiving team to concede a point in favour of better field position