No your thinking is wrong.

The plants MUST have those fan leaves. It is THOSE that absorb the light energy which is THEN converted to plant energy.

The plant will NOT be able to produce adequate buddage without those leaves. Sorry...but it is true.

The smaller growths from the secondaries do not have enough foilage to power the growth. THey get it from the fans. Then the secondaries will sprout and shoot up.

If there are no fan leaves...there isn't even energy 'catching' foilage to spur her on.

NEVER EVER cut a fan leaf. Trust me...I have done it. And will never do it again. You let those fan leaves stay on the plants until they are dead, yellow, dried and withered.

Everytime. All the time.

Follow that fundamental rule of cultivation.