I firmly believe that Jar Jar was always intended to be a character that stuck with our protagonists through the entire prequel saga. But then everyone hated him so Lucas was pretty much shamed into barely even showing him in the next two. Clearly he didn't have the conviction or passion for the character to have kept him in regardless - which just shows that Jar Jar as a character wasn't thought out at all and none of it was planned out because the next 2 were written Jar-Jar-less and still function (or don't as may be the case).

So as it stands, his role in the prequels is compromised as he didn't fulfill it for more than the one film, which to me makes him completely pointless and it's a bit odd to have someone be so significant in one film yet become pretty much a cameo role in the rest.

His only role even within TPM is to introduce us to the Gungans, and when it comes to it, I'd remove the whole lot of them too! The battle with them vs the droids is ultimately pointless so why have it? Let's just have one human population on Naboo and leave it at that.

My vote would be to get rid of him. Better yet, replace him with some character Ady is adding throughout the saga. Replacing him with a recast Anakin and rejigging it all so they meet him on Tatooine would be my wish, but I've harped on about that enough :-p

I'd agree that in the average fan-edit, removing Jar-Jar would be impossible, however Ady is no doubt going to do some major rearranging and, I assume, flesh much of it out through refilmed elements. This isn't just another fan edit where we need to retain their reason for getting to the Gungan city and then into a submarine etc etc. In his edit, none of this might happen. Maybe something completely different that we never imagined happens.