I agree with MVP and your anecdotes - less bloat, all the better, but from a UI/UX perspective, let me give you a few examples of what usually gets thrown out in a mobile first design:
Dropdown menus - Mobile first almost always means multiple clicks to get to the same place, which is more annoying on a slower browser.
Commenting system - still yet to see a decent one that I would one on a mobile interface
Flash/animations - like it or not, moving images grabs attention but does not translate well to mobile.
Page width - 1440 pixels on my shiny screen, but text is stuck in a 200px box that forces me to scroll down. Flexible width usually gets thrown out when you add sidebars and ads.
Large Buttons - Great for mobile but I'd rather see context that a sign up button taking half the page
Related content links - Especially for blogs/news websites.
Inline images - My primary annoyance with this article which is ALL TEXT. Mobile design says dont take up an entire screen view with an image. Web first design says even if the current text is boring, people will scroll down if they see an interesting image.
I honestly believe that having separate approaches will allow for better UX, time and cost permitting.