Don't forget that there's a whole music genre (or several) out there that relies totally on DROPPED or downtuned instruments, and deviate from regular tuning, both bass and guitar. However, it's moreso about the tuning, than the reliance on "one more string down low". It's mostly in the heavier rock styles and metal (not to speak of the latest fad, called "djent").
Remember, that Jimmy "Flim" Johnson was the bassist that made the first 5 string recording in 1978, with low b, but that was jazz fusion. On his Alembic.
Even way back in 1973 when Black Sabbath released "Sabbath Bloody Sabbath", the title tune went in C #. Tony Iommi, the guitarist, used to drop all his tuning to Eb, in order to make strings softer due to his finger damages at fretting hand, and on top of that, used a "drop d" tuning to that. I e his low e-string was tuned down to C sharp. Thus, Geezer Butler, their bass player, had to follow him down. There's no way he played a regular tuned bass tuned in E, and played this C# note on the fourth fret on the a-string. He did tune down as well, and changed string gagues accordingly. He didn't need any fancy newly built basses for this (extended scale), but used his plexiglass Danelectro, Rickenbackers, Fender P or J basses, for this. You can check this out for yourself by checking out their low dropped tunes on iTunes or Spotify. That the resulting tone, or timbre of the bass wasn't that good, was another matter and maybe a recording limitiation from the gear used in those days. I think even it started on the "Masters Of Reality" album, where he dropped to C#-F#-B-E tuning. I think this is the first one I've heard of doing this that early. Also, I've never ever heard of him using a 5er. Maybe very briefly*, but he's been a 4er most of the time.
Most nu-metal bands today, their bass players doesn't use any 5ers. They use 4ers but drops tuning down low. BEAD or else. Even Warwick Warlord has F# as a lowest string. But still a four. I do think that this has more to do with that we like open strings. I e that it is better to get a new four string bass, with maybe fan fret, or extended scale and still use only four string, but tuned down a step or two. Or more.
I did not forget to tell you that I still use both 4 string and 5 strings. 50/50 of the time. I swap between them. I feel equally at home with them. Even if the 5er is a Dingwall combustion. The thing with the fiver is that when bringing it to any gig, I have to make sure the amps and cabs are up to snuff too, you have no use for a low b-string if put through a 10" 80 watt combo, if you can't line it out to any PA. And when and if I play a fiver through those amps, I don't rethink my playing all of the time and goes "Hey, I have to watch it, so my fingers don't go down to that b-string...might as well uses it as a finger rest for this gig..."
Maybe we'll have to re-phrase and change out the wording in that old catchphrase "There's no money above the fifth fret" to "There's no money below the fourth string?"
*http://www.talkbass.com/threads/geezer-and-5-string.578683/