"Modern Web Development" does not mean "Works in Webkit", and it does a disservice to future/novice developers to reinforce that notion. What's dominant now was not in the not-too-distant past, and may not be in the not-too-distant future.
You misunderstand. This was how modern web applications are written. I know very few people who write modern web apps but do not use Chrome for it. The reason is that Webkit has the best tools. Cross-browser independence isn't the point, since when I'm developing I'm using only one set of tools.
When Mozilla ships better developer tools than Chrome, I'm sure there will be posts just like this one. The fact that developers prefer Chrome is not a failing of developers; it's a failing of Mozilla to provide compelling tools.
Firebug is pretty close, but you're right.
I don't know much, but I don't understand Mozilla's effort to reimplement firebug natively. Right now their solution seems unusable and far beyond firebug.
They're reimplementing it because Firebug is an unmaintained mess.
Mozilla is just in an unfortunate situation, where Firebug's ground-breaking functionality was duplicated as a first-party feature of other browsers. So now as Chrome Inspector continues to add more and more deep functionality, Firebug is hampered both by being third party code and subsisting on Firefox's addon API.
I acknowledge WebKit's monopoly on the mobile landscape today, I make no claim whether it's a good thing or a bad thing, that argument would distract from the reality that if you want to make a mobile web app work well, you need to build it on webkit and debug it on webkit