There is no real answer to this, but l can help explain it to you.
People prefer Single Battles over Double and Triple battles because Single Battles is the most standard way of play. Double and Triple battles were not introduced until Gen III and Gen V respectively, and Single battle has always been there, so it is the original way of battling.
Double and Triple battles also add new ways to play, and like you said, requires more strategic thinking.
Everyone knows how to play and work out Single Battles, so most people will play in the mode they are most comfortable with.
Like me, l do not/did not train a team for competitive Double or Triple battles, so l will tend not battle people in that mode of play.
That's really all there is to it! Single battle is universal!