No. This allows a content delivery network (such as cloudflare) to host content on your behalf without having to have direct access to your private key material.
The main use cases you may be interested in are to 1) make it so that users connecting to you get a faster experience - since they can connect to a geographically nearby cloudflare server, rather than your distant server and 2) make it so that cloudflare can absorb large denial-of-service attacks that your server couldn't otherwise cope with.
Cloudflare probably is easier than running your own servers and configuring them correctly - I don't know since I haven't used them myself.
But it sounds like you're not very familiar with the importance of the private key. If anyone else other than the bank obtains the bank's private key, the bank would consider that a serious failure, since it means others could impersonate them. The whole point is that you shouldn't give your private key to anyone else, and that without that key, others can't impersonate you.
This "keyless SSL" scheme allows the bank to set up an entity it controls which knows the key. This entity delegates to cloudflare the ability to pretend to be the bank on a request-by-request basis, without divulging the key to anyone. If cloudflare gets compromised, the bank can stop that delegation on demand, the compromise is closed and the key is kept safe.
To serve SSL for your domain, Cloudflare needs a certificate for your domain issued by an accepted CA, which someone needs to buy.
The only way for them to set that up would be to become a CA, get browsers to accept their master certificate and then issue their own certs for their clients.
Yes, but you still need to buy and give them a certificate, right? The question included "can offer SSL for free without buying certs", which is not possible, AFAIK.
