Hmmm, interesting idea. It leads me to another one that can be done currently without “raw providers” cooperation. We already have kind of a public key of the server. It is its SSL certificate 
Just imagine that original raw https response (before SSL decryption) would be temporarily included to the oracle response. Then everybody could compare if oracle correctly extracted the answer from the http(s) response. I am not the expert, but SSL encryption uses client’s ephemeral crypto-key and server’s public crypto-key. When you have the raw http(s) response and the ephemeral client’s crypto-key you can check yourself that the response really comes from the server.
So to sum up. Even if you will use an Oracle you don’t trust, you can always check if the https response comes from the server (SSL certs check, response decryption).
Or… we could have specialized Oracles that will only decrypt responses from particular domain. That oracle can prefetch domain SSL cert and provides responses only for that domain. If that would be standardized, then Miners would check every Oracle’s response against that SSL certificate (provided by Oracle). Miners can’t be responsible to fetch SSL cert, they need to be provided with it. Then miners would to another useful work they are paying for. But I can see a bottleneck (or opportunity), the original HTTPS request, SSL certificate and client’s ephemeral private key will need to be provided by oracles to miners, probably another kind of fee will need to be introduced for that bandwidth.
Oracles will be very important part of smart contracts. They will evolve and as you can see they will be quite bandwidth hungry. Chainlink might really gain a traction because they can do that logic off-chain (or on their chain to be more precize). Maybe it would be better to focus on a good and seamless integration of Aeternity with Chainlink (and other oracle solutions) and let that logic to be done by Chainlink nodes? Aeternity, maybe it is a time to make some partnerships?