If you're looking at IKEA, couldn't you use the high kitchen cabinet? Those are nice and sturdy. For example you can buy a Sektion kitchen cabinet almost matching those dimensions exactly for around $70. Of course you have to add on the doors, hinges, shelves. If you choose the lesser expensive cabinet door the price would be the same as that laundry cabinet or maybe a few dollars less. Instead of holes, you could situate the shelves for the hamper height and have shorter doors so that there is space to drop things in without opening (if that is what you're going for.)

I haven't seen that at IKEA but it's a neat idea.

I'm installing the Sektion cabinets in my laundry room and have room for one high cabinet big enough for laundry baskets.

sorry if i misspoke i am looking for a similar cabinet NOT from ikea