My MIL hosted my baby shower at my house. It's true that you don't have to worry about getting your gifts home, but you do have to worry about the clean up! Before and after the party.
I was around 7 months and huge! So I was exhausted after our shower/BBQ. We had basically a family shower, where men and children were invited along with the women. It was more of a house party, plus shower games! I remember hoping that everyone would go home soon so I could rest, but I did have lots of fun, and I didn't have to worry about driving home late after the party. There are pros and cons, but if I could do it again, I would choose a different venue than my home, just so I don't have to worry about cleaning. :) The house was a mess after, since we served alcohol and of course there were kids running around.
I think if you are having a "traditional" shower with women only, it might be less messy and chaotic. But no one thought that I was hosting my own shower, especially since my MIL sent the invites herself and it clearly said her name on them.