So you have to pay DNSimple for the service plus whatever each domain costs per year? I'm not understanding their pricing scheme very well, it seems.
There are two separate costs: one is the domain registration and the other one is the hosted DNS solution.
With the hosted DNS solution you get access to stuff like the one click setups I mentioned earlier, API access, domain forwarding, vanity name servers and who knows what else. Keep in mind you can use their DNS service even if you don't register your domains with them.
After dealing with registrars for a long time I've realized that paying extra $5 per domain per year is totally worth it if you don't have to deal with companies like GoDaddy.
I'm not familiar with the Amazon service, but if it's $1 per domain per month then you'd save $0.7 for every domain using DNSimple.
EDIT: I should link to another HN discussion on the subject: http://news.ycombinator.com/item?id=2753471. One comment that resonates by jbyers: "Read your registrar's terms. See if you still want to save that $6 a year".