So if you don't trust online banking/payment, then you don't buy anything from online sites like Amazon? Also, I guess you don't trust ATM? How do you think your deposit/withdrawal from those ATMs update your bank account? Do you think USPS takes all those transactions and deliver them to your bank?
Remember, delivery of your snail mail is done by a person. How many times have you received a mail that was meant to be delivered to your neighbor? I've had my neighbor bring me my bank statements before I completely switched to online statement. I also agree with booch221 and Meatman--2008.
You stated going online is "the easy way"? It's actually the other way around. I take the responsibility of retrieving my bank/credit card statements. I take the responsiblity of making sure my payments are made. I agree you need a proof of payment, but you can still do that online. Whenever I purchase online or make payment online, I aways print to a PDF for the "proof" you're referring to. And yes, I ensure those "proof" are protected. I have RAID6 NAS for home cloud and I also back them up to discs (if you really want a proof that you can hold in your hand, then you can go ahead and "burn" trees by printing them).