You could, you'd just have to be wary of how large the header metadata would be. If you had a single Cloud-Optimized GeoTIFF of the world with internal tiles up to zoom 14, the header metadata could be a few MB, which wouldn't be ideal to load in every client.
Sad to say it but these days loading a few MB to a client is par for the course. I don't think it's a reason not to try and get this working - the range header trick does sound particularly relevant to this format.
Thanks! The text is still relevant but those demos are a little old. If you're curious these demos are from last week (using Cloud-Optimized GeoTIFFs under the hood to serve image data quickly):
Just like the SQLite example: https://news.ycombinator.com/item?id=27025829