But what would be the incentive for other site owners to use it then? It seems like in this scenario, the only time anyone would want to use the tool on their live site would be when they are sure they are getting an A+, any other sites that don't care about that score just wouldn't add the tool and any changes that might lower that score would presumably being taken care of before rolling out to production.

It seems like it would just turn into unnecessary bragging for the site owner. I wonder if the scoring would still be useful for development though, or if they would just try to fix as many problems as possible anyway.