Which it quite often is. Like the example they show with the early-game check with the queen, putting the king in check by placing a totally undefended piece within one square of the king is (usually) a suboptimal move, and the king taking that piece will (often) be the most optimal way of getting out of check.

In this variant the attacking piece will effectively be protected by how bad its move was. Creates some interesting incentives - the only way to checkmate is a move that is normally not optimal and has only one way out of check.

Right, so your check should be in a context where another move was mate in 1