Lets try some role reversal

what would the outcomes be if yoda granted obi wan's request to fight palpatine instead of darth vader.

in other words

in ROTS

Obi wan vs palpatine
and Darth vader vs yoda

Obi Wan and Vader would both be dead, then when Yoda tried to take out Sidious either Yoda would run away or die. Then Yoda might have stayed on Tatooine to watch Luke if he'd lived.

Either way though, the OT would have been very different had this happened.