Why Do I Need a Better/Lighter Road Bicycle to Train For 'Fitness'?
Rob, you are correct that a heavier bike will give you a greater fitness benefit over the same distance.

The only real counter-point I have is that the most effective bikes for fitness are the ones that get ridden. So, if some reason a lighter bike would more fun or appealing to you (while still be a "good enough" commuter), than a lighter bike could be a better choice for you. 

In my experience, extra weight is not noticed much for commuting, so I'd rather have the durability of CroMoly over aluminum or carbon, and the practical benefits of fenders, racks, lights and bags.

An anecdote: My wife rides a bike with electric assist. You might think electric assist would reduce the fitness benefit, but opposite is true for her. She takes more trips because she has electric assist (including carrying one or two children plus cargo), and thus ends up riding-- and pedaling-- more than if she had an unassisted bike.

Some will suggest that you should get a lighter bike for "social" riding. That depends on who you ride with and what their fitness levels and interests are. I'm personally a stronger rider, and prefer to ride with my wife, parents and older friends, as well my children. For me, having a bike that's a bit heavier improves the social parity and helps to me ride naturally closer to the same speed with the people I prefer to ride with. If you want a hang with "Group A" club rides, lighter would be way the go instead. 

Whatever gets you out riding the most is best bike for you.