You missed a couple of things...
First, your scheme requires the ability to export the private key from the device (even if it is encrypted). This is poor security practice.
Why? If RSA and/or ECC are really "uncrackable", and is mathematically proven so, I fail to see the problem.
generate and store the private key in a tamper-resistant secure chip
Absolutely true. However, it has to be tamper-resistant because this chip stores PLAIN-TEXT KEYS. If they keys are stored encrypted, the the key encryption key has to be stored in pain-text. These chips often have limited memory, so you can off-load secrets from the crypto chip into the host, but this key is encrypted using a chip-specific key. What you call "poor security practice" is baked into the TPM spec.
Second, why should the manufacturer have the ability to decrypt the user's data?
OK. You have a point here. However, if you accept the postulate that somebody with a warrant signed by a judge has the right to break into your stuff, then you have to trust SOMEBODY. Maybe not the manufacturer, but a private company with a staff of lawyers to protect the rights of the customers.
On the other hand, if you don't accept that postulate, then you probably trust nobody. I, for one, would like to help law enforcement if possible, provided that they can get a warrant. I would not trust them with the keys, but would be OK with having somebody else decrypt my info as long as my legal rights are respected.
Fourth, the manufacturer's private key will eventually leak.
Hmmm. There are a several companies that make a living issuing certificates that have managed to keep their private keys secret. There is already an ecosystem around this problem Why would this one use case be any different?
Fifth, the manufacturer cannot be trusted to represent the owner's interests by requiring a legally-sound warrant before exercising their backdoor
This is closely related to your second point. However, I could imagine that not protecting the customer's privacy would result in some backlash against the company, as it should be. Transparency would be the problem here. Once again, maybe have a trusted 3rd party be the key holder. Maybe some organization like the EFF could have the key-holder and charge the police $1,000 to decrypt the data.