Well more important than 'to strap or not to strap' was achieving proper bar set-up. After a bunch more mountain riding I realized my bars were still way too tall, so hope this does the trick. I also realized I rarely if ever touch the strap, so I opted to ditch it.
The reason that they put a strap on the bars is so that you have something to tie your additional gear to I use if for taking a down sleeping bag (in a compression sack) with me, not that I have any concerns with a Polaris possibly breaking down in the wilderness and having an impromptu camping adventure.