Nope, you don't need your own AS for this to work, nor do you need to use BGP. They support static routes too. BGP peering support is actually "beta" according to Cloudflare: https://developers.cloudflare.com/magic-transit/get-started/...
You do ideally want your own /24, though even that's not a hard requirement. And it can be provider-assigned space as long as your provider is willing to sign an LOA for you.
As for competitors, there are a few that start in the low 4 digits per month for similar services. That's not to say Cloudflare doesn't have anything unique to offer though, they're great at scale and standardization.