I think that's an east coast thing because we've never stayed in a rental that had sheets or towels or any other kind of linen without paying an extra fee. To OP also make sure to check the sizes of the beds at the house before you leave home. We rented a cabin in Maine and knowing the cabin didn't supply linens brought sheets from home, well, wrong size beds :

$100 later we had two sets of scratchy icky colored sheets we couldn't use at home.

.
We also bring our own pillows, except this last time when the cottage listing said it came with pillows but lo and behold they weren't usable for sleeping so we had to track some down. Luckily there was a
Walmart nearby that had some for $3/ea.
Before you bring casserole pans make sure there's an oven; we've stayed in two cottages that only had toaster ovens and one that the oven was so small it only held small pans like an 8x8.
If you have kids make sure to pack sand toys they're very expensive if you buy them at the beach. Also check to see if boogie boarding is allowed if it is make sure to bring your own from home they cost about twice as much at the beach.
Aside from spice other food items to bring from home - ketchup and mustard and any other item like peanut butter that you won't use the whole container in a week.