It is very common for live-aboards in the marinas here around LA. It is so much cheaper than renting and is a decent way to live if you don't have a lot of belongings. To give you an idea of some prices, if you wait for a good deal you can get an old sailboat (1960-70s) for under $1,000. I got a 24' 1968 Del Rey for $500. It would be better to have a longer one to live on, but you could manage on mine.
Instead of rent you pay a slip fee which is anywhere from $8-15/foot per month. I pay about $200/month to keep my boat in the marina including electricity. Around here a small studio apartment goes for usually around $1,000/month. So that probably answers your question as to why people do it.
You can get a mailbox at the marina and get your mail there. They will also hold your packages from Fedex or UPS for you. They have shower facilities, laundry rooms, and most have lounges with couches and TVs where you can hang out.