While guitar and bass may look similar, they certainly don't do similar jobs. Guitars are built for chords, amongst other things, whereas it's unusual to play chords on bass - the notes are too low, hence sound muddy.
That's where 6 string basses start to appeal. With the top strings well into guitar territory, chords can sound good - especially triads with a low bass note and two other notes on the top two strings.
Tuning wise, most folk prefer to keep the same 5 fret differences between all strings, which on guitar is deemed non too practical. So, on 5 string basses, BEADG, or more rarely EADGC are the ones that are 'standard'. The 6 string encompasses both those, thus stretching the range - BEADGC - all 5 frets (P4) from each other. That makes playing patterns so much easier, as everything is instantly transferrable, unlike on guitar.
You could, of course, tune any bass to anything you want - one of my 4 strings is BEAD - but with perhaps a change of string gauge, anything goes.
So, please don't think of any bass as a guitar extension - its job is different, and it gets played differently accordingly. Some of the string/fret theory is the same, but we don't generally transfer that theory from guitar to bass.
You may, or may not find the high C much use, depending on what you play, and your style. But the low B is deemed a useful asset by a lot of players, including myself.
You could go the whole hog, as a friend of mine did, and obtain a rare 8 string - F♯BEADGCF - but I think that's taking things a little too far, especially considering the plank that's needed for the neck/fingerboard. And the decent amp/speaker that's required to cope with the wide range of pitch!