I remember an old conversation about the Jedi Order seen during the prequels hadn't always been so institutionalized and conservative, but that the last Sith War drove them in that direction.I would have liked it better if Jar-Jar had started out as the goofy prat we know him as but slowly became a competent Jedi. In TPM he could have had his last big screw-up which forced him to reflect and get serious about in things. In the end he would be a quirky Jedi odd-ball who can also fight in a badass style and get bussiness done.
Why have Jar-Jar be a Jedi? To inject a litte bit of life into the Jedi. All of them were so serious and devoid of personality it would have been nice for one of them to still retain a sense of humour. Kudos to Obi-Wan for still being capable of empathy.