Help me clear up my brain fart

"Never cross control!!!"
"Keep that ball centered!"
"Never use more than 20 degrees bank!"
"Too high on final - go around. Never slip unless its an emergency
landing."

These are things that were hammered in my head by my numerous CFIs
during pattern training as a student pilot. Now that I have my PPL,
you would think I should have this understood. Unfortunately, now this
is really twisted up in my head.

Was all that preaching JUST to reduce the chance of invoking a deadly
spin in case the wings are accidentally stalled? It seems to all
contradict everything about slips on final and the famous
"low-wing-into-the-wind" crosswind landings?

In my mind, as long as I keep my airspeed sufficiently high and keep
the nose pointed down, (ie. keep my AOA under control) things like a
steeper banks and routine slip to landings should be relatively safe.
Right?

Thanks,
Ekim