striker position

Why would putting a left footed striker in a right side position make him likely to score more goals?

Sometimes. The in-game tips tell you this too. Try it yourself.

Hell I would prefer to play in the left slot if I was lucky enough to play a striker and with a striking partner. Then one could try to cut inside a lot more than you would normally do

There are two immediate benefits I can think of:

1. By switching wingers and thus "inverting" them, you change your attacking pattern in a bid to disrupt your opponents defense.

2. You now attack outside in, which forces the opposing wingback to defend on their weaker foot and creates room inside by creative dribbling for strong AMs and strikers to move into and attack.

Note: You'll more likely than not want to make any winger with a strong foot opposite their assigned side an inverted forward, as crossing wide from the byline is very difficult with your weak foot. Be wary of how this affects your attacking shape: You're going to have more bodies in the middle of the pitch but no width unless you have your wingbacks overlap. This can be good if you have strong playmaking midfielders, but will create more congestion that makes fast play difficult.

Note: You'll more likely than not want to make any winger with a strong foot opposite their assigned side an inverted forward, as crossing wide from the byline is very difficult with your weak foot. Be wary of how this affects your attacking shape: You're going to have more bodies in the middle of the pitch but no width unless you have your wingbacks overlap. This can be good if you have strong playmaking midfielders, but will create more congestion that makes fast play difficult.

Hmm. So when playing with IFs cutting in, it might be better to play with a DLP, and a slower (passing) game?