I would be in favor of any new technology for the web requiring TLS. It provides both a carrot (of new features) and a stick (of falling behind competitors) for people to get off their asses and secure the web from a whole host of attacks.

Even if your page doesn't have sensitive information on it, an insecurely loaded page provides an attacker the avenue to inject potentially malicious code. This will be the case until the entire web is HTTPS-enabled.

Aren't there any security risks when using this over HTTPS, considering past attacks like BREACH and CRIME?

CRIME: TLS compression can reveal private headers, like auth cookies. Fixed by turning off TLS compression. Not applicable to HTTP because HTTP never had header compression.

BREACH: Response body compression of a page where there's (a) something attacker controlled, (b) something private and unchanging in the body can reveal that secret, and (c) response length is visible to an attacker. Doesn't require HTTPS.

If an attack applied, it would be one like BREACH. Which isn't surprising: this is a direct replacement for "Accept-Encoding: gzip / Content-Encoding: gzip" and so we should expect it to be in the same security situation.

I think as long as you're not compressing secrets and attacker controlled data together you're fine.

Good incentive for people to use https IMO.