The 4-4-2 structure that many elite sides defend with off the ball is typically to accommodate lazy attackers, where they're basically already playing with 10 men off the ball. So same principle applies with a 4-4-1 and it's the easiest shape to change into mid-game. I don't think you can carry many players who won't run off the ball as the opposition overloads will eventually kill you. Ideally your centre-forward knows how to play as a single striker for a team that has less of the ball - someone who can press, win fouls, hold it in, stretch the play. That makes a huge difference. Keeping the ball is key and the best way to achieve that with 10 men is a compact shape to allow your team to overload in smaller areas - i.e. by making the pitch smaller. In any 11v10, you'd also want to afford their technically weakest player the most time on the ball, to ensure the opposition's build-up is as clunky as possible.
All of this would be worked on in training as it's a pretty standard scenario to model on the training ground.