The proper analogy for the internet isn't burgers or the Panama Canal. The proper analogy is to compare internet service providers with the power company. The former charges you to send ones and zeroes through their lines, the latter charges you for electricity sent through their lines. A kW/h is a kW/h regardless of what it's powering, just like a kbps is a kbps regardless of the transmission's content. Wouldn't it be ridiculous if power companies were allowed to charge you different rates to power your washing machine depending on its brand?
So you've never paid an electricity bill? The power companies charge different rates based upon demand relative to capacity, which is similar to what the ISPs are proposing.
In theory I would have no problem with an ISP charging variable rates for data usage based on their network load, assuming it was implemented evenly, fairly, and was well-regulated by the Federal government the way FERC does for electricity markets. But that's not what ISPs are doing- Comcast throttled Netflix to promote their own Xfinity service, for example. Net neutrality isn't about pricing, it's about preventing providers from forcing a content-based tiered internet on their users.