I have an opinion I would like to share:
I think that if you feel you NEED more than 4 strings, you're either doing something wrong, or you should be a "lead bassist."
Reasons:
1) The range of a standard 4 string is 3 octaves, E (open)-E (21st fret on G). This will give you at a 2 two octave range for any key you play in, no problem. Most stringed instruments in an orchestra will have a similar range. (With a couple of exceptions)
2) Since most melodies only range within an octave to octave and a half, you should have no problems keeping up with providing harmonic structure and counterpoint.
3) Most, if not all, metal bassists I have seen who play 5 strings, don't need the extended range so much as they need the 35 in. scale so they can down tune/ drop tune. I never see them use the G string unless they are doing some kind of solo work. Still not that common in metal.
4) The extended range issue can be fixed by tuning the bass to 5th's. It is similar in scale to a cello, so this would be fairly easy to achieve. Plus, you only get an extra fourth anyhow, so the utility is questionable.
5) Many, many very great bass players can eek out some great stuff on only 4, even when playing "lead" work. This tells me that the bass, though only 4 strings, is still a very flexible instrument.
6) Never carry what you don't need. If you're not doing some crazy Claypool stuff, or some Jeff Shcmidt insanity, the extra strings don't really add anything but bulk to your instrument. So if you're doing structure and counterpoint work, the extra bulk will present more technical challenges than a bass player really needs.
7) If you really want the thunder of a low B, you can get plenty of balls with a good low boost at 40Hz, or a sub-octave pedal that's dialed in just right. Or both!
I have a two-word answer that actually rebuffs all of your points perfectly:
Anthony Jackson
Simple answer, but he does it. But to be more specific:
1. Covering a 3-octave range presents far more technical difficulty on a 4 than on a 6. A 6 also gives you a greater range, and to be frank, who cares what range other instrumentalists use- unless your plan is to play their music rather than write your own that is.
2. If you're only worried about providing harmonic or melodic playing within a 1 to 1 1/2 octave range, then you really only need a one-string bass. Pianists only need 18 keys. Etc. Or you could just rid yourself of the arbitrary limits that someone else places on you and play the notes you want to play. Imagine if someone came on the forum telling you that you're doing it wrong because you play with a four-string rather than a one-string

Your idea also implies again that you're playing someone else's music rather than your own.
3. Okaaayyy...how the metal players you've seen play their basses doesn't have much to do with anything, including the metal bassists on TalkBass that DO utilize all of their strings.
4. If you're focusing solely on the extended note range that an extended range bass offers, then you're missing most of the picture. Not only will tuning in 5ths make playing more difficult due to the extended reaches you would have to make, but it would not offer the ease of transitions a 5/6/7/etc. offers, it will not offer the different note tones you get by playing the same notes on different strings, it will not give you the extra harmonics, etc. The list goes on.
5. Most guitarists could probably eek out great stuff with only three strings. I've heard soulful sax solos that only use four notes. Does that mean they should limit any further flexibility? Mark Sandman did a great job in Morphine using only a two-string bass. Are you ready to cut off two strings on your basses from now on?
6. That's kind of a silly statement- if someone is using their extra strings just for craziness, then they simply don't know how to play their instrument. If they can't work the extra strings into their regular playing, then it is their failure as a player, not a failure of the instrument. It would also mean that most pianists are doing it wrong in your opinion, because most pianists won't hit a fair portion of their keyboard during a set.
7. Boosting the 40hz range will not transform an E to a B, or any other note for that matter. An octaver also does not sound the same as the actual note- I've owned several analog and digital octavers and can attest to that.
P.S. Keep this in mind: I learned how to play bass on a 6 string. Queer way to start, eh?
Definitely an uncommon way to start. Unfortunately, from your post, it shows that you never learned its functionality in a musical sense at all. Playing a six and finding it doesn't work for you or offers you options you don't need is fine. Thinking those options aren't necessary for others is not.