We had the same experience as Kevin, in the same places. In Sequoia, the Rangers were adamant that we use the bear boxes, and they came by to check us in the evening after supper. In Yosemite, it seemed to be more of a yawn. Since we are Easterners, where the bears are no larger than your average ox, we used the bear boxes religiously in both places - it didn't make sense to do anything else. And we tossed a blanket over everything in the car that was even vaguely rectangular - the rangers said that the bears think that anything with straight edges is a cooler, even if it is a case of 10-40 motor oil.
For us it was easy. We have a 40-qt TE cooler (Walmart, about $79) that we carried with us during the day as we drove around. The Explorer powered the TE cooler, and kept things nice and cold. When we got back to the TM, we brought the cooler inside, and prepared supper out of it. After supper, we simply slid it into the bear box. Worked great. A regular cooler would do as well, except that you have to find ice.
My wife also found a cardboard box, and loaded it with ANYTHING that has a smell. Soap, shampoo, deodorant, toothpaste, floor wax - I thought she was going to stuff me in there! Before we went to bed, she slid the cardboard box into the bear box.
There is a bear box at every site, it is big and easy to use ... why not?
The good news is that there are plenty of appetizing tent campers in both campgrounds. If the bears are going to bite anyone (and they don't seem to be actually interested in people!), those guys are the easiest targets. While we were there, three tent sites (but no tents) were invaded. But no canvas campers, TMs, or hardsides. And the ASPCP assured us that no people were harmed in the making of that vacation.
Don't worry about the bears. Go, enjoy, be a bit prudent - and feel comfortable and secure in your TM. We did. We loved both places.
Bill