He didn't side with Anakin.
He sided with Darth Vader, a Sith Lord and sworn enemy of the Jedi.
Once Vader takes a lava bath Vader's true identity would be a secret to all but a chosen few.
It's so handy for Palpatine that Anakin got his identity burned off it's almost as if he planned it that way.
Perhaps having Palpatine telepathically prompting Anakin to jump (like Obi-Wan prompting Luke to blow up the Death Star without the computer) could put a bit of a line under that?