Also, will the teams get penalized for having a groove disappear like they did in the past? I mean, if you're going to force the teams to use just one set of tires for both qualifying and the race, then you can't force them to have a discernable groove visible on each section of the tire, can you?

Me thinks NOT, not with the 1-tire rule.

if the grooves don't to exist at the end of the race.