You sidestepped it, rather than really solved it: you got rid of the CNAME issue by trading it for a proxy availability issue. It works--of course it works, it's literally why cloudflare exists--but now your service availability is directly tied to cloudflare's availability. And cloudflare glitches often enough that plenty of people run into their 5xx pages on a daily basis across the web.
So you traded an intermittent problem (only relevant when an IP change occurs) for 24/7 guaranteed service outages for a (probably very) low percentage of your intended demographic.
Cloudflare provides CNAME flattening without enabling Cloudflare CDN on a domain, so you only have to be dependent on their DNS infrastructure, not their CDN/proxying infrastructure.
Would you like me to edit it so it says "Now your service availability is tied to not just the global DNS system that literally anything that wants to exist on the web with not just an IP but a named host relies on, but a secondary routing entity that sits on top of standard DNS and does fancy things"?
Because I'm pretty sure we all know what I meant when I pointed out using Cloudflare means gaining a convenience at the expense of being at the mercy of third party outages.
So you traded an intermittent problem (only relevant when an IP change occurs) for 24/7 guaranteed service outages for a (probably very) low percentage of your intended demographic.