First of all the public internet is "best effort" at best when it comes to 'QoS'. Some providers will provide better than "best effort" for RTP and SIP packets. But, there's no guarantee the next hop (router down the line will do that, so everything should be considered "best effort" in other words pray the packets get there timely, if at all. Concealing those packets in a VPN will guarantee you that you will always be stuck at best effort though because the ISP can't see them and prioritize them. Second, security has nothing to do with it as Mitel doesn't send RTP in the clear, so you can't just load software and listen to conversations in progress.
Prioritizing where you can, i.e., the local switch and router, can help with traffic that is competing at your local site. For example, if a couple users start downloading files and saturating the link. Once it leaves your site you're at the mercy of the ISP and that can be a difficult place to be. A cheap home router in it's default config will send everything best effort, so if you start enough downloads and make calls with the teleworker phone, the garble will start.
Excellently-worded response. I saved it in my email templates.
I remember reading a wikipedia article that mentioned the reasoning behind the lack of qos on dsl/cable/residential connections (all I remember is it mentioned dark fiber, the market downturn of 2001, and after 2001 providers stopped prioritizing different types of connections, whereas previously bandwidth was carefully prioritized, and now bandwidth is an all-you-can-eat smorgashbord [btw, you can't just keep throwing bandwidth at a qos problem afaik. It can help, but not solve it]). If anyone knows the article I'm thinking of, please let me know.