The flaw in your design is that when the PC dies, you can no longer decrypt the backup because you just lost the private key.
I see it as a requirement rather than a flaw. If my data can be decripted after I have lost my key, then other people had copies of my key. It is a well known and documented fact that we can't trust everyone with access to the other copies of my key.
You never see my requirements or feature requests or responses on user serveys, or those from people who ask me for help, because your product doesn't meet my needs and gets discounted in the first round (along with almost all of your competitors).
Some online backup companies in the past have solved this by having you store your private key in yet a 3rd party "escrow" location, so you don't have the only copy and yet the company with your backup data does not have the private key either. In essence that is what Backblaze does, just in an "easy to use" way. We store the private encryption keys on one particular server, completely separate from your data. The data is all on "pods". Is it as secure? I don't think anybody can claim 100 % security, we do the very very best job we can.
Yes, the escrow solution has exactly the sames flaw as Backblaze's model. Security is fundamentally flawed as soon as users lose control of their key. All that effort ensuring keys are never writen to disk provides some protection against hackers, but can be completely bypassed by authority. The list of people and organizations that can gain or already have such authority is always surprisingly large. You are doing the very very best job you can for the model you have chosen to implement.
Fixing key loss problems requires guiding or ensuring that the user to keeps copies of their key. Maybe you can even offer to keep a copy for nieve users, or make some pocket money selling keyfobs, but if you start from the position of compromiable keys you can't support people with a healthy dose of paranoia. And that is becoming more and more of us. We are stuck with encrypting *before* we use your service, which makes your service less usable and less attractive.
I always find it sad when people advocate blacklists to protect their sensitive data. 'Encrypt your most sensitive data first'. It doesn't work, as it assumes you know what your most sensitive data actually is and don't make mistakes. You need to protect *all* your data by default, and open up data you determine to be not sensitive when necessary ('Share this photo with friends', 'Sync with Contacts').