Private Messaging on Twitter

One of our clients asked me if I thought it was effective to reach out to new Twitter followers with a Private Message. I wasn't sure at the time but I've been curious as well. My personal experience has been that the majority of the PMs I receive are automated and impersonal. To me Twitter is such a short lived experience, I usually just reach out to followers publicly to thank them for following.

Hmmmm... is there anything interesting in my Twitter PM?

My inbox is mostly filled with offers and sales pitches. The better PMs say hi, link me to a website or another social network. These seem to be the most friendly. The worst and more common want to sell me eleventy-trillion followers - ugh! Twitter discourages spammy, automated messages and abusers can have their accounts suspended.

Why is there never anything interesting in my Twitter PM?

The first PM is selling me a very specific type of insurance, and the second wants a retweet. The third is nice but clearly automated. The fourth is selling me something, and the final request is to like a Facebook page.

From where I sit, private messaging in Twitter is so filled with automated messages, it's just not worth my time to check it. 

UPDATE: Just to be clear, I still check it! Never want to miss out on something, but I do sure get a lot of offers for 30K twitter followers for $10. ;)