Nope. The Pi makes a lot of sense for a simple web server with a robust SQL/NOSQL database backend running with Node/Go. If you have a good internet connection with a good upload speed, you can easily run a server able to take a couple of hundred hits a minute. It is certainly a better option than using the cloud for prototyping, where a wrong for loop can instantiate loads of instances and bill you a hell lot.
The Pi does not make sense for any level of consumer-targeted production (dev, stage or live) beyond "oh hey, it works." "A couple of hundred hits a minute" is also not impressive in the least, even for something of the Pi's stature.
I also don't think the stack would matter all that much at this point - IO blocking would be happening at the application level, not the architectural. Node, Go, Ruby, Python, PHP ... it really wouldn't matter. SQL versus NoSQL is also a non-issue in this case.
I also wouldn't take something very underpowered instead of the cloud just because I hadn't configured my cloud host to keep things within reason (ie no autoscaling at all, which is what you'd expect for hobby-level prototyping.
tldr; don't eschew better options for the Pi unless you don't understand how your cloud host works.
I agree it makes no sense for consumer-targeted production. I have played with the pi and run a small robot to collect intermittent data from twitter and store it on Mongo, which I can remotely access using the web service.
At the same time, I would not want to go all the way to the cloud for such a small thing. I guess it depends on the use-case.
