You outsource it because clouflare have more locations than you so offer lower latency and can offer it at a cost that's cheaper or the same price as doing it yourself.
To the contrary, CDN pricing will usually beat cloud provider egress fees.
Common example: you can absolutely serve static content from an S3 bucket worldwide without using a CDN. It will usually scale OK under load. However, you're going to pay more for egress and give your customers a worse experience. Capacity isn't the problem you're engineering around.
For a site serving content at scale, a CDN is purpose-built to get content around the world efficiently. This is usually cheaper and faster than trying to do it yourself.
They will be doing a mix of peering both across free PNIs and very low cost IXP ports, with the reminder going down transit like Colt or cogent. Probably average cost of the order of about $1 per 20TB of egress in Europe and NA markets.
The thing is with edge capacity is that you massively overbuild on the basis that;
It's generally a long ISH lead time to scale capacity (days not minutes or hours).
Transit contracts are usually 12-60 months
Traffic is variable, not all ports cover all destinations
Redundancy
So if you are doing say 100Gbps 95%ile out of say London then you will probably have at least 6+ 100Gb ports, so you do have quite a bit of latent capacity if you just need it for a few hours.
