That would indeed be an alternative: do a full king-capture test after every King move. But it would be more expensive, as a King usually has several moves.

It's more than that. I do a full king-capture test for every pseudo-legal move by every piece that can move. My code works like this.

1. It goes through every piece from the side that can move.
2. For each piece on the side that can move, it calculates the spaces within its range of movement. This is an optimization to keep it from checking for legal moves to every position on the board.
3. For each space within a piece's range of movement, it checks whether the piece has a pseudo-legal move there.
4. For each pseudo-legal move, it tries the position and checks whether it places the King in check.
5. It checks whether the King is in check by checking whether any enemy piece can move to the King's space. As an optimization, it returns true as soon as it finds one check.
6. It checks whether a piece may move to the King's space by calling its function for the move from its location to the King's space.
7. Divergent pieces are handled by writing them to behave differently when the movetype variable is set to CHECK. In the following example, the function for the White_Pawn first checks some conditions any Pawn move must meet, then handles capturing, then continues to handle non-capturing and en passant moves only if movetype is not CHECK.

def White_Pawn
remove var ep
and < rankname #1 var bpr
and < rankname var ep rankname #1
and == filename var ep filename #1
and checkleap #0 #1 1 1
and var ep
or and checkride #0 #1 0 1 == rankname #0 var wpr
or checkleap #0 #1 0 1
and empty #1
and != var movetype CHECK
or and islower space #1 checkleap #0 #1 1 1
and any onboard where #1 0 1 == var movetype CHECK count var wprom
and <= distance #0 #1 var fps
and > rank #1 rank #0;

8. Pieces with non-displacement captures are handled by writing two different functions for them and using the value of movetype to call the correct function.

So you would have to do enemy move generation several times.

Since my code uses piece functions, this is not a big problem. In tests I ran yesterday, my checked function ran 1000 times in under half a second, and the checked subroutine got called 1000 times in close to a second, and this was on a position in which the King was not in check, which meant it never broke out early. Since your code does not use piece functions, it may handle the evaluation of moves more slowly, which will also cause it to evaluate check more slowly.

Testing whether a destination contains the King is not any more expensive than marking the destination. And to do it, you only need to geenrate all enemy moves once.

This optimization might be helpful when not using piece functions, but one thing about it concerns me. While it might be helpful in determining whether a move by the King would be into check, I'm not sure it will work for revealed checks. It is because of the possibility of revealed checks that my code checks for check for the position resulting from every single pseudo-legal move it finds.

I suppose one optimization that could be made if it were needed would be to identify the pieces that might possibly check the King at its current location, then limit the test for whether a move by another piece places the King in check to those pieces. This could be done by making a short list of every enemy piece whose range of movement contains the King's location and having the checked function use it instead of onlyupper or onlylower. If this list were empty, it could even skip the step of trying out a pseudo-legal move and testing whether it places the King in check.

However, this might not work for non-displacement captures in which the capture occurs outside the piece's range of movement, such as the Coordinator capture in Ultima. So, I have to balance efficiency with the work a programmer has to make to use a piece in a game. The brute force method I use helps reduce the work the programmer has to do to make different kinds of pieces work with it.