Is bigger tyres worth it?

Part of traction is driver related.
I personally (when itchy) have spun the tires at the track all the way down. Less coffee and more suspension adjustments have gotten 225/60-15 coopers (old Cooper street tires) to grab better than cheap slicks. But nothing grabs better than hot and sweaty fresh slicks. lol! Basically a lot has to do with driver. Get confident with a bunch of runs and dial the whole car in. JMHO.