My hardtail has a 34t ring and doesn't look like it would clear 36. I think newer xc bikes are made with up to like a 38t ring in mind though. And a 10t little cog is like having two more teeth on the chainring, and tire size matters, so for example 29x2 with 36x10 is the same gear inches as 42x11 on 28mm road tires.
There's this "gravel race" that happens occasionally, and I've always used my xc bike over the cx because of the forest road descent at the end. Really rough, loose, and there are always a bunch of flats coming down to the finish. Since the last time it happened I put on better brakes (still rim) and got some 40s for general/gravel riding. Made it a lot better and I might consider riding it on that one. Rocky mountain roubaix is coming back next year and I'm probably riding the cx bike on 32 slicks as it is turning into more of a gravel race.
And rigid, drop bars, 40ish tires does get you a pretty good amount of speed and efficiency on flat roads compared to flat bars and 2" tires. I generally don't like riding my mtb across town and such even though it's a light xc race bike with flimsy, fast rolling tires.