For those unwilling to grind down the engine case to accommodate a 12" rear tire, can you use an 11" back tire and would performance be noticable over the stock 10" tire?

I need to get new tires and was hoping someone had info on this. I was looking at the Michelin City Grip 2 (120/70-10) but it looks they also sell the 11 inch version no one seems to mention those here? Maybe there's a reason haha Thanks in advance!