I run my own servers. It is not that difficult and while it can take up time, it is also a very valuable experience. The biggest benefit: I learned a lot about server administration, stuff that gives me an edge when doing development. I also learned a lot about operations. Most system admins that I encounter are happy to discuss server arrangements with me, rather than scuffing at "another silly developer who doesn't know mysqld from grep".

I also know the exact limitations of my hosting platform: I know where and when things are backed up. I know who has access to the users' data. I know what kind of redundancy is built-in.

If you want to focus on "building a kick ass application" get yourself a cheap VPS, install Debian or Ubuntu on it, and start coding. Once you get to the point where you are paranoid about your VPS provider disappearing or having downtime, set up a hot standby with a different provider and automatic failover.