There is something very appealing in the idea of running own web server on a small, cheap device like RaspberryPI and pushing it to the limits. It's of course far more reasonable to just buy a hosting and don't bother about it, but how great would it be to host applications on your own server infrastructure? :)
The bottleneck wouldn't be the device, it'd be your internet connection. Higher latency, no uptime guarantees, bandwidth limits, contract restrictions, etc.
Plus, unless you already have a 50 or 100mbps connection at home for other reasons, getting that internet connection speed will cost you more than a VPS somewhere (usually). (And, it'd be 100mbps downstream, but your upstream would likely not be more than 10-20mbps.)