Why would you need the original HTML for dev tools to work? Maybe there are ones I've never seen but the ones I use are using the DOM rather than the original HTML string.
One case where you would View Source in addition to using Dev Tools is debugging how the browser is massaging your source HTML into the DOM, for example by inserting missing <tbody> elements. Validating your HTML mostly addresses this (I'm actually not sure about the <tbody> example, I would hope the validator at least issues a warning), but isn't something you necessarily want or can do with, for example, user-uploaded HTML snippets.
You can use dev tools to view the network tab to find whatever URL Pandora is using.
You can use dev tools to find a media elements src attribute.
To see the JavaScript sources... You check the dev tools.
If anything, in the days of JavaScript, the HTML source will missing a few things.