I also get a few of these each week, I am very wary of them and never respond. My blocked list is huge.
In trying to figure out how such a scam might work I’ve come up with two possibilities :
Scenario 1
The scammer entices you ( their target ) to accept their contact request. They eventually (after various messages over and back) entice you to unwittingly divulge some information that they can later use in a email phishing attempt. The chances of their phishing attempt being successful is greater due to this additional information provided by your good self!