I used Debian stable as my primary OS for a couple of years. While I was just fine without the fancy desktop, at the time Firefox was stuck on version 3.0 even though 3.6 was available.
I don't know what the situation is like now, since I haven't used linux on my laptop for a couple years, but if I were to go back, I would want something like Debian stable, but with an updated browser.
I can imagine it being more useful for things that are easily fixable/less critical.
I was running a testing desktop, and X updated in a way that broke the proprietary nVidia drivers (nVidia's fault -- not Debian's.) That was quite annoying to suddenly have to fix. Those types of issues (though rare, even in testing) would be nice to avoid.
Debian's idea of stable really means super duper rock-solid extremely stable. Which is ok, but I had a hard time running newer software on it. I now use Debian Testing, which is most people's idea of stable. Several debian-derived distros are based on Testing, so it's probably ok.
I am using Crunchbang, which is based on Debian stable. It is trivial to download and install either Firefox or Chrome from the internet, and they automatically update themselves (FF since v12; the betas have had auto-update for longer).
For a more general solution you could look into apt-pinning, but there are some downsides depending on which way you go about it.
I don't know what the situation is like now, since I haven't used linux on my laptop for a couple years, but if I were to go back, I would want something like Debian stable, but with an updated browser.