The rook-pawn draw only works when the attacking king is far away. With the king on f4 White mates or wins the pawn by combining checks with king approach, since stalemate is no longer forced.
Same material as the previous drill, but White's king is on f4 instead of h8, and now White wins. The stalemate defence depended on White having nothing better than quiet moves that cover g1 and g2. With the king nearby, White can give checks that also bring mate threats, and when the black king goes to h1 the white king steps to g3 or f3 and mate follows on g2 or along the first rank.