Why would you need your own DNS?
Control of TTL values is on example. Most registrars use 4 hours these days but it used to be that 24 hours was the value used by most (with not option of anything else). That can be a minor convenience if you expect to move things around much. I have all mine set to 5 minutes (not a great idea for anything high traffic, but nothing of mine is). If you know what you are doing running a small DNS service is no great hardship at all (though it is surprising how many people don't get it right). Custom dDNS is another reason you might want this (though I think some registrars and specialist DNS hosts offer this for little or no cost these days).
In my case it costs nothing as the three bind instances I run live on geographically separate machines that I already have for other reasons (home line, external web service, backup location) - if you have no external resources already then you'd need to pay for somewhere to host a secondary server of course (cheap, reliable enough, and fast enough VPS services are common so that needn't be much cost - though a specialist DNS services needn't any more expensive these days either and will likely be more scalable than anything we setup manually).
There really isn't much of a performance hit by recursively resolving DNS - it all gets cached anyway.
[1] http://unbound.net/ (other servers may also work for this purpose)
[2] It protects against a resolver that lies, but race conditions (e.g. NSA/QUANTUM) are not affected. Hopefully, DNSSEC itself protects against poisoned results, regardless of the method.
Because I have frequently seen provably-wrong results from other resolvers, and some highly-suspicious results from 8.8.8.8 on occasion (though I haven't checked particularly often).
The point being, unless you're proving the results with DNSSEC (or similar), you can't trust any source.
I use and recommend doing both, as there's very little downside to running your own resolver.