That's a good point. The reality is I would run the heck out of a 375 can if I had one, but really I'm trying to figure out whether said 375 can would work well enough on my 223, or do I just need 2 new cans
It certainly wouldn't NOT work, and I'll never advocate for "just buy both" if your budget today can't support that.
But a few points of consideration:
A 375 bore would be far better serves with a larger volume can versus what is essentially a K can for that caliber.
A 375 will require a larger thread pitch and permanent shoulder be added to your wife's rifle, whereas the 6 ARC can go 1/2x28, or my preference a 5/8, one of those is likely what comes on the rifle already.
If you decide to do a mount swap on the can instead, you'll need to buy an extra mount (if it doesn't come with one). You'll also need to buy the extra end cap.
You also really want your components assembled and torqued down consistently, and torqued onto the barrel so it doesn't back off. To swap from one rifle to the other, you'll need to pop the barrel threads, then wrench off what would likely be carbon-locked mount and end cap, install the new ones, and wrench back into the new barrel.
And since you already have a silencerco, you know you're not doing that at the range because the can gets too hot.
None of which are insurmountable issues, but it's very reminiscent of the "buy one $3k scope and a QD mount, and use it for all of your rifles" marketing jargon of 10 years ago. You can make it work, but you're compromising at both ends, and the manufacturers know that the inconvenience will ultimately lead you to buy one for each rifle anyway.
If you have the expendable funds available, get a svelte, sexy can that will live on your wife's gun, be it a 6mm or 30 cal, then one that would truly impress you on the 375. Just my opinion.