I have had several overnighters and I always enjoyed morning fun. However, this was without any prior request on my part and the woman always initiated, so I marked this down as 'go with the flow'. One aspect of overnighters I have not experienced is "wake up in the middle of the night sex". I have several overnights with an SP that was mentioned having offered this, but she never initiated it with me, and I found out that the reviewer in question had specifically requested it. It makes sense.
Like others mentioned here it can be enjoyable with SPs you know well and are not the type to go on 'autopilot' after the first SOG. Generally speaking, if at the end of 2-3 hours I wish I had spend more time with her, then next time I will go for a 6-8 hour date. If I still feel like I wish I could have extended the time, then I know she is a good candidate for an overnighter. There are also other small indicators, like if she invites you to shower with her (versus you having to ask), if she pays attention to your needs and takes initiative on starting subsequent SOGs.
Also this may or may not make a difference, but for longer dates and overnighters I think booking a nicer hotel room motivates the SP to spend more private time with you.