Been meaning to post a reply here for a bit, just to throw in my bit.
'The electric bass' is an instrument, 'bass' is a function that anything that can access the bass register can provide e.g. piano, euphonium, etc.
The range of the 'bass' function is somewhat up for debate but for the sake of argument say it typically ranges from as low as a low B to perhaps open G/5th fret D string(?)
The necessity inherent in fulfilling the 'bass' function is that you need to have access to and use that range of notes. Following on from that, 'the electric bass' need not and should not necessarily be limited to a function, however it would be appreciated that once you leave that register, you are no longer fulfilling the 'bass' function.
The ERB is very much like a piano in that it can access all/most registers, hence it's great for arranging, fulfilling different functions etc. BUT unlike the piano it is very difficult to hold down two very different functions at once (outside of tapping at least), making extra strings seem superfluous at various points, hence when you play low comments of 'why do you need all the higher strings' and when you play high 'why don't you just get a guitar'.
In short? My humble opinion is that the ERB is a different instrument, and as such should be treated as one, that it's not something to 'get' or 'not get', that such a question is akin to saxophone player asking a violinist to justify what they play. They may share similar construction and appearance but they are not the same.
Note: Not attacking the OP, I think it's a completely valid question, and this is my valid opinion.
Now... to bed!
Mark
EDIT: By the way Dood, your bass rocks!