Sure, maybe, you could be right, but you are talking about the real world, and this is not the real world that we are discussing.
All this discussion about tires "in my league" doesn't seem rational to me. I'm saying that given Michelin is a prominent licence in the game, as prominent as any car manufacturer, it stand to reason that the developers used Michelin tires as a reference. So, since there is a Pilot A/S, Pilot Super Sport, and Pilot Cup 2R as Michelin's Sport tire, I imagine those were the tires used as reference for the SH, SM, and SS.
Looking at all possible tire data across all brands is just too much. Also, the Pilot all season tires are standard equipment on many sports cars, like the c8, so again, it stands to reason that would be the reference for an SH tire.
CH would be Michelin Defender or the Energy Save A/S, because those are the harder compound in the passenger car range.
IMHO trying to compare the real world to this game is misguided. If the cars feel real, and the times seem reasonable, that's about as far as the tracks times can go. There's too many factors, and unknowns, to use real world times as an accurate measure.
Let's not forget that time is a massive factor as well when it comes to tire tech. I know that with motorcycles, a modern soft street tire is as grippy (if not more so) than a racing tire from 30 years ago. I wouldn't be surprised to see similar leaps in cars. So, again, the lap time as a measure might be the wrong metric to measure against (especially if you are comparing older cars)