Can someone clear this up for me—
If the wire I had wasn’t in Romex and was in MC to would be fine?
The wire insulation is good to 90c, the romex sheath is the limiter at 60c which bumps down the amperage allowance in this case to 55a compared to 75a in MC?
The answer to your question is "yes".
#6 NM-B cable is rated for 55 amps. When de-rated for continuous loads, it is only good for 44 amps.
#6 MC cable is rated for 65 amps (as is THHN/THWN-2 in conduit). When derated for continuous loads, it is good for 52 amps.
(90˚C insulation rating is only used for de-rating when running wire in hot environments or installing more than three current carrying conductors in a conduit. The terminals on the TWC and residential circuit breakers are only rated for 75˚C.)
If you ask "why", it is due to all the stuff that "Tronguy" discusses in is post above.
But just think about it for a minute. An intermittent load might heat the wire, but then the load shuts off and the wire has a chance to cool down, so it can handle more current than a Tesla Wall Connector, which might be drawing 48 amps for well over 3 hours.
The NEC has decided intermittent loads are loads that are on for less than 3 hours. These decisions are the result of years of experience, investigations of fires, testing, research, and so on.
And why can MC cable handle more current than NM-B? They both have the same wire contained in an outer sheath. Well, the metal sheath of MC cable can dissipate heat better than the plastic sheath of NM-B cable. And individual wires loosely contained in a conduit can dissipate heat better than the wires that are tightly contained inside the sheath of an NM-B cable.
If you overload a circuit a little, the insulation will not "melt" and will not suddenly burst into flames and burn your house down. Wiring is supposed to last for a long time. What happens is, over a long time the insulation becomes brittle and crusty, and it can crack and eventually two wires might start arcing which can, and does, cause fires.
I suspect the NEC code is conservative enough that a few percent of overload will not cause much trouble, but why not follow the code and do it right? The cost is not much more to do it right.
BTW, whoever installed your electrical panel did a beautiful job, and your installation of your TWC is also very nicely done.
NM-B (Romex) is used because it is easy to install. There is nothing wrong with it. But for installing a TWC that is going to run at 48 amps, with a 60 amp breaker, I think it is easier and better to use either conduit with THHN/THWN-2 wire, or MC cable. And #6 SE cable can also be used but it might be harder to get. MC is a little harder to work with, but easier than conduit if it has to be run where there would be a lot of bends or fished through existing walls. #4 NM is also sometimes hard to get, and very hard to bend in tight places like the TWC. And you have to buy 4-3 NM because 4/2 is not made by most manufacturers. MC cable might be hard to find at Lowes or Home Depot, but is easy to get from electric supply places or Amazon.
Hope this is helpful. Take care.