I think the only butlers I have experienced were at the Burj al Arab, where there was one per floor, and Zimbali (pre Fairmont). Both were pretty pointless.

We had something similar at the Maldives Park Hyatt - there he was called a villa host. Although we had very little cause to use his services he used to come around in the late afternoon to deliver the daily "treat" (usually something sweet to eat) and used the opportunity to make sure everything was to our satisfaction. That worked very well because if we had any small niggly problem that didn't warrant picking up the phone, we could convey it to him then and leave it to him to sort out. He was perfect for his job - charming, willing, courteous, never obsequious or over-attentive. I guess getting the right staff for this role must be a challenge.

Amanpulo had a similar person dedicated to guests in the casitas - but the execution was not nearly as good. Your allocated person was as likely to be unavailable as not and you ended up dealing with whoever answered the phone at reception anyway.