thats exactly my thoughts as well sidious is very hands off. hes more like a chess player in my opinion he sees the enemy forces and sends troops where he needs them he doesnt do any dirty work. In ROTJ he knows the rebels are attacking the shield generator but does he go to stop them? no he sends an extra garrison to ambush them.
Well if Yoda wasn't around, then I think Sidious would do absolutely nothing BUT command troops around.
The fact that Yoda needs to be killed means that only Sidious has the power to do that. Obviously he thinks he kills Yoda but is obviously mistaken. Once he "knows" Yoda is dead, he knows there is nobody strong enough to challenge him.