Would a one off use of a computer to generate paper wallets then wiping the hard drive work? Paper wallets would be a lot easier to hide in multiple places.
No, because they can just take the paper wallet and have the bitcoins.
This is basically what happened to Ross Ulbright when the FBI arrested him, but instead of paper wallets they used his online account that he was already logged into.
That is why you only unlock your wallet when you are in a secure environment, and only for a brief period of time.
A secure environment is relative to your situation. If you are running the FBI's #1 criminal syndicate, with the entire US government and every politician after you, a secure environment is NOT a public library in a major city. In that situation a secure environment is something much more remote where you can be sure you will have enough advanced warning to re-lock or close your wallets. However if you are your average bitcoin user a secure environment is in your home, maybe using an off-line computer if you're very paranoid.
Paper wallets if you use them, need to be stored in a very very secure location that only you and those you absolutely trust know about. This is not your basement or even a security deposit box. Paper wallets are also something that you never ever go back to unless you absolutely need them, they are meant to "store and forget".
Ross broke many of these best practices. A great thing about bitcoin is they can be secured absolutely, but require correct usage by the owner and are susceptible to user error.
I think that Ross was trying to avoid connecting to SR while having any connection to his ISP at all. If the FBI were to somehow execute a 0 day attack on him then they would only be able to see the IP address of the library, but if he was somewhere in private then a 0 day attack would be able to identify him specifically. I think he gave up one security rule in order to prevent a possible other attack against him.
I really don't think he ever predicted that Silk Road was going to be as successful as it was. It appears that the government put a lot of effort and resources into finding out Ross's identity and gathering evidence against him, effort and resources that would likely not be put into trying to convict a small time drug dealer. However all they got was information from simple mistakes that could have been prevented if he had known how much of a wanted person he would become in the future.
I would argue that if Ross had known how successful Silk Road would become, he would likely have created a throwaway email account on TOR to register for that drug forum to post about Silk Road (that the FBI agent found, the one that originally had Ross's gmail account, but was later changed to altoid@altoid). If he had done this then I don't think he would have ever been caught.