Fascinating to me that you picked Thriller as an example, as MJ even demonstrates a 2&4 clap during the song.
https://www.youtube.com/watch?v=sOnqjkJTMaA&t=5m0s
Curious what you mean by half the claps? Would this involve clapping only on every fourth beat, only on every second beat, or am I completely misunderstanding?
(Come to think of it, this seems very song-dependent. For instance, I definitely find myself clapping on 2&4 to "Thriller" and "I Heard It Through The Grapevine". But I think I'd still clap 1&3 to some of my favorite classic rock and metal songs. Also, I felt 1&4 pretty strongly in that Harry Connick Jr. clip. Maybe they're just clapping too fast: if they were only doing half the claps, I think 2&4 would feel more natural.)