Keyboards are actually some of the least versatile tools out there.
You can certainly make all kinds of different sounds on your keyboard. But, unless you use a different controller (which you can also do on any other instrument), each individual note can only be louder or quieter, and can also be turned on or off.
Keyboards often have sustain and volume pedals and usually band controls, but these affect all notes together rather than a single note. For bass, as with other instruments, there are also numerous pedals and controls available that affect all notes together.
The bassist can slap, legato, tap, harmonize, use a pick or fingers, and most often have a couple of options to play the same note on different strings, giving it a different timbre. Bassists can play vibrato if needed. The bassist can vary the attack on the strings, the sustain of the notes, and the way any note is produced without much thought. Bass can also, of course, have all kinds of effects like a synthesizer.
In terms of keyboard range, you need a long keyboard to cover the range of the bass, which can also be five or six strings.
The bass player can jump an octave or a third without moving his arms too much. Very few keyboardists will be able to play a standard bass part with one hand. In general, the bass part can be very awkward and technically difficult for the keyboard.
The point of the bass part is that you have a musician who is dedicated exclusively to bass. A keyboard player playing bass with his left hand will never get the same quality rhythm. You may have an instrumentalist who specializes exclusively in playing the bass keyboard, but in that case, you won nothing against the bass guitar. In doing so, you have lost all the dynamics and expressiveness that the bassist puts in without even thinking about it.
Bass is naturally suited to bass lines that simply move any song. There are some synth bass parts that reach the same level, but this is usually not the case.
The sonic possibilities of the bass are almost endless, but bassists are not inclined to use them to their fullest at any given moment, because this is not the job of bass in rock music. Bass and drums come together to provide a solid bottom that always makes a big difference between great bands and mediocre ones.
Thus, the bass guitar as an instrument does not need more flexibility, more range, or more sounds than it already has. It employs players who feel the rhythm and can tirelessly maintain it during a three-hour performance.
However, in this age of pop songs and vocalists who depend on AutoTune, I would bet that a good percentage of performers (perhaps up to half of studio pop and hip-hop songs) use keyboards for bass.
I played in a band without a bass player, when we only had the left hand of the keyboard player. We still sounded great, but we didn’t play traditional rock, but more eclectic material. However, a bass player is absolutely essential for many genres. I currently play bass in a surf rock band and the sound would be bad if the bass played on the keyboard. However, The Doors sounded great live with Ray Manzarek on the keyboard playing bass with his feet.
Keyboards in the 60s were organs and electric pianos. Even then, there were groups without a bass player. However, I play keyboards and pianos myself, and the last thing I want to do is do the dual function of playing the bass lines …