This new SSL scheme is mostly security theater. There's no particular reason to encrypt traffic to most web pages. Anyone with access to the connection can tell what site you're talking to. If it's public static content, what is SSL protecting? Unless there's a login mechanism and non-public pages, SSL isn't protecting much.
The downside of SSL everywhere is weak SSL everywhere. Cloudflare sells security theater encryption now. All their offerings involve Cloudflare acting as a man-in-the-middle, with everything decrypted at Cloudflare. (Cloudflare's CEO is fighting interception demands in court and in the press, which indicates they get such requests. Cloudflare is honest about what they're doing; the certificates they use say "Cloudflare, Inc.", so they identify themselves as a man-in-the-middle. They're not bad guys.)
If you try to encrypt everything, the high-volume cacheable stuff that doesn't need security but does need a big content delivery network (think Flickr) has to be encrypted. So the content-delivery network needs to impersonate the end site and becomes a point of attack. There are known attacks on CDNs; anybody using multi-domain SSL certs with unrelated domains (36,000 Cloudflare sites alone) is vulnerable if any site on the cert can be broken into. If the site's logins go through the same mechanism, security is weaker than if only the important pages were encrypted.
You're better off having a small secure site like "secure.example.com" for checkout and payment, preferably with an Extended Validation SSL certificate, a unique IP address, and a dedicated server. There's no reason to encrypt your public product catalog pages. Leave them on "example.com" unencrypted.