Actually, with DigitalOcean, you get quite a lot of bandwidth for the price. Additionally, their transfer limits are high (1TB for the $5 instances), and overage is only $0.02/GB. If you combine this with something like Route 53's anycast latency-routed DNS, it can work very well.
That question is 2 years old, and refers to an "unlimited bandwidth" fair-use policy. DO does not have unmetered bandwidth, so is it still relevant?
Their current policy FAQ says they do not even explicitly forbid Tor exit nodes, although there is a stern warning, so why would they disallow a proxy configuration dedicated solely to your site?
I'm assuming that's a paid CDN with clients like CloudFlare or Akamai, not you distributing your website to multiple datacenters in order to serve more clients faster. If you happen to use CDN like DNS features to route the client to the closest Digital Ocean datacenter, you're probably in the clear.
Maybe it can work. I'm still a little skeptical. But I don't see why you would ever want to deal with managing all this infrastructure yourself when there are many established providers that can likely do a much better job at a comparable price.
Managing the infrastructure is definitely where it falls short, but if you can get it done quickly it can be very cost-efficient for smaller projects. Three $5 DO boxes can easily handle > 1TB per month, which will cost over $100 on most CDNs.
CloudFlare's hit rate is predictably terrible for large binary files. We actually use DigitalOcean + Varnish + S3 for serving downloads from mods.io, since the files are relatively big and the site has such a low margin. Traditional CDNs (we were using Fastly) are not scalable cost-wise for that particular site.
Managing the infrastructures is quite easy with Ansible, Puppet, or whatever your flavor of config management is. You can also take advantage of anycast DNS and GEO targeting by signing up for a free NSOne.net account. That would probably shave $5 off the total.
If you have quite low usage yes, and if you have quite high usage you probably won't be running a CDN on DigitalOcean anyway, but there's an in-between point where CloudFront is pretty expensive (by about 10x over the roll-your-own solution, depending on some assumptions about traffic).
If you build a smallish network of, say, 10 of the $10/mo, 2-TB-traffic DO servers, and can manage to spread the load such that you use an average of half of the free allocation, you pay $100/mo for 10 TB. Cloudfront would charge you $1200/mo for that data transfer. Obviously it's not the same level of reliability or ease of scaling, but it's cheaper enough to be vaguely intriguing—$1200/yr versus $14k/yr is non-peanuts!