yes that is true, flexibility, I tried that once myself, unfortunately as time passes I realized that self hosting my websites aren't helping me that much. I just gave me additional tasks and worries. Cause the Internet Connection in our country (Philippines) is not as stable as in the US or other countries (I suppose).
We'll my comment above is just true for myself. Cause most of the times when I am outside the house, I worry most about my server for several factors.
1. There might be a power Interruption, and my computer might shutdown and the website will be down. I decided to Get a 1 hour UPS. for that purpose. but fot those power interruptions longer than 1 hour, and there are cases where I am 6 hours away from home. It's a big trouble.
2. Internet connection might go down. (like I said DSL connection in the Philippines is not that stable) and even costs higher.
3. Cost of Electricity to power up your computer 24hours a day may also be considered.
Uhmnn we may not consider the Cost of internet connection you will have that anyway even though you don't host at home.
Actually I'm still hosting some sites of mine at home using a WRTG54 Linksys Router and a Speedtouch ADSL modem, hosting at home using these is very easy, those that have less than 10 visitors a day, and those that requires a very low bandwith. If these Increase, you need to think twice. If you are just serving a small website and your visitors are your friends and/or relatives at least you can tell them that.
I have both Static and Dynamic IP on my two connections.

there are really quite some advantages and disadvantages over. It's realy up to you and to consider these factors.
Good luck.