I was an AD controller for 25 years and practiced MFF on many occasions. I can state factually that, apart from pre-planned engagements, it never worked effectively. The logistics involved in successfully scrambling and assembling the package in the correct location to obtain the correct tactical position on an opposing force package were so involved they weren't worth the candle.
Many more kills and success to place the lightweight fighters on their own VISCAP or under airfield control for point defence to engage the bombers that got through than try and get them mixed up with the enemy fighter sweep.