For the life of me, I can't think of a reason I would ever use the physical Apple Card. If it is a place that doesn't accept Apple Pay yet, I would use my Double Cash card (2% back). Even if the place accepts Apple Pay, but you try to use the card, it will only give you 1%. You'd think using the card at a place that accepts Apple Pay would still count as 2%.
I've got a few different cards, both for lender and network diversity (and keeping old accounts), but I have closed some accounts over the years to simplify things. At this point, I have a few cards that earn more (4% or 5%) in particular categories, so they get priority there (either quarterly or all the time) and then the fallback is the Apple Card for Apple Pay transactions that don't fit the above area.
After that, the remaining things like utility bills, a Walmart/Sam's Club trip, etc. are the tough ones because I have a few 1% options. I looked at getting some sort of "everything else" 1.5% or 2% card, but can't justify opening and managing another account for such low spend at this point. That leaves me with a few options for those 1% transactions and I'm still trying to figure out a strategy—put them all on one card for consistency? Spread them around? Put them where they could potentially earn a little more than 1% when redeemed for gift cards (Discover/Chase)?
Nonetheless, I leave my physical Apple Card at home, since it's not really pulling double-duty in my wallet like some other cards.
What if you have to shop at a place like Walmart?, they have their own screwed up payment processing methods at the checkout. I would not even fathom the way that their credit card transactions are processed; between the cashier and customer, you have to go through some serious hoops to perform something that can be resolved with a double-click on the Apple Watch or a few taps on the iPhone. But some people still do it, although I have honestly never seen any customer use Walmart’s credit processing method in-person.
I'm not sure what Walmarts you're going to, but for the most part it's like any other that do physical card transactions—insert/swipe when ready, wait for the approval, remove? If you're talking about Walmart Pay, I haven't used it and haven't seen anyone use it the few times I go through there, so I can't speak to the nature of that. That does look like an awkward, messy dance between POS, cashier, and customer.
I tried the version using the Sam's Club app (you scan your items, pay in the app, and walk to the door and they scan your phone and a few select items to "prove" you didn't steal anything), mostly because one card was offering $10 back for trying it with some purchases. It's not bad, but an Apple Pay button in the app would've made it that much nicer...they already have my purchase history based on membership, so why not?