The only real disadvantage I see myself is that if an IP block (of your host) gets RBLed, as was mentioned in another thread, you might get caught up in it. One advantage I can see for some people is that the headers will backtrack to the host, instead of to your ISP (assuming that they are different).
Otherwise, I don't find it to be that big a deal one way or another - as long as the mail goes where it should, that's my major concern.
On the second point, about having a backup for your ISP's mail server - good point. If your ISP continually has problems keeping the mail server running, using SMTP through your host would be a good thing to have available.
I use SMTP through my server and find it quite convenient. Even though my ISP's servers aren't down often and are generally reliable, most any company's servers will be down a bit every once in a great while. I can switch back and forth in just a few seconds. Its very convenient and also makes good sense to have an alternate means of sending or receiving e-mail.
My ISP, on the other hand, hasn't had an email outage in quite some time - so long, that I haven't remembered (lucky me).
I think SMTP availability/use really depends on personal preference. I know quite a few people like Duster, who really like the convenience of having another outgoing route. And then I know people like me, who don't really care one way or another - if it's there, great. If not, there's the ISP, web mail, etc.
One point about "having" to use your own ISP to send mail rather than the server you have paid for (and I have yet to see an Alabanza host tell people in advance that its that way) is if you use several ISP's you may find you have to change your SMPT setting each time you mail. Also the portability of being able to add an email account to another users email system and the (I have experienced this) added explainations to customers if you resell or consult on a server that uses your ISP instead of the "convention" of mail in and out both at www.where-ever.com