Business guy here with experience in fulfillment. Yes, some companies do indeed try to screw people out of promised rebates. And those companies are complete morons. One key reason you would want to pay rebates is that in the fine print there is usually a disclaimer saying that by claiming the rebate, the company now has information (name and address) that can be used to understand who is buying their product. It’s called marketing intelligence.
Manufacturers usually have no idea who actually buys their product from a retail outlet. By collecting data through rebates they can (watch out for big brother now) market additional products to the person who bought the original product.
If you are concerned about privacy, I’d recommend not filling out the rebate forms. If you don’t think the big brother aspect is a problem, go for it and hope that you get a smart manufacturer who actually fulfills on his promise.