I've never seen a reason to switch to Voice over IP. The sound quality isn't as good, it's not really much cheaper, you may have to change your existing phone number, you don't have a phone if there's a blackout, and (for some VoIP services), you have to be able to tell the operator your location if you call 911. It may never happen, but if I have to make an emergency call, I'd like it to go as smoothly as possible.
Having said all that, I do work for a phone company that has a substantial number of people using traditional phone lines, and is just starting to face local competition from VoIP providers, so I could be very biased.
We had Vonage in San Diego when Lise was there and I was in Oregon. We talked every night for a long time, so I've probably been on the receiving end of Vonage as much as anyone.
About half of the time there was a slightly annoying echo of my part of the conversation. Only I could hear it. Still, compared to what we would have paid for even a $.02 per minute plan, it was a huge benefit for us that it was unlimited long distance.
Towards the end in San Diego that cleared up, and I've not heard it since. We brought the Vonage unit up here to Oregon with us and we still have our San Diego number active on it, so it is a local call to us in Oregon for any of our San Diego friends.
We have a local number here for people who are here and keep the Vonage line for calling out on long distance. With our family all over, it is worth it for us just to know that our LD bill will only be the $25 Vonage bill each month.
I've considered keeping only one line, but with the power and internet here less reliable than you would find in a major city, I'm hesitant to do it. I'd be OK with it only because we have two cell phones as backup, but I wouldn't get it as a single line with no other option.
Have you considered Skype?
BTW - you can generally keep your old number unless you live in a small Exchange. We couldn't do it here, but we could have in San Diego.
Sounds to me like your boss just doesn't want to do the job she should have been doing for the last year or so, presuming the worker in question (a) is a long-time slacker and (b) reports to your boss.