This is nice, and the lack of push notifications can be seen as a feature – less distractions! One possible solution to that issue is to build a push notification server into the desktop version so they wouldn't have to store your credentials.
One thing that keeps me from using Sparrow for OS X (or any other desktop client) is that they download every email, and I don't want to spare the 7 GB of hard drive space for something I don't need every day. Mail for iOS lets me choose to store only the last X messages on the device, but I haven't seen that option on any desktop client.
Wouldn't that also delete the from my IMAP server (in my case, Gmail)? I'd also be worried about deleting the messages from my [All Mail] folder, which is what I have a real issue with (my inbox is rarely very large).
One thing that keeps me from using Sparrow for OS X (or any other desktop client) is that they download every email, and I don't want to spare the 7 GB of hard drive space for something I don't need every day. Mail for iOS lets me choose to store only the last X messages on the device, but I haven't seen that option on any desktop client.