Yes, I'd miss it. When I moved over from 4-strings to 5-strings I changed how I approach the fretboard. I play across the neck rather than down. Seldom do I play things that you have to play on a 4 down in the first or open position down there (unless it incorporates low B or C)...and utilize the 5th string to play across the neck in the 5th-to 12th fret range. I have no desire to go back to a 4 string.
My response is similar. After decades of playing primarily a 6-string I tend to play more across the strings than up and down the neck. This relates more to the C string for me as I don't tend to play the B string much above 5th fret, because I don't like the tone. I believe the problem is inharmonicity. For the same reason, I don't generally play the E string above about the 10th fret.
I play jazz standards quite a bit and am expected to solo, so I play up the C to about the 15th fret quite a bit (maybe a bit higher). I would definitely miss the extended range and tonal variance. Obviously I could play those high notes on the G string of an extended range instrument as well , but I am not really that familiar with that area of the fretboard. The extra strings makes it much more efficient to cover the required range without the need to make huge shifts on the neck.
I do think the B string is more essential than the C string for most players. There are many songs that really benefit from the extended low range. Also there are many times when singers cannot covers tunes in the original key. The B string makes it possible to transpose the original bass line down without having to invert intervals. This can be very important with an iconic bassline.
I played 6-string in country band for a couple of years and there were plenty of lines that benefited from the low B and high C. There's an irritating Geico commercial currenlty on TV with an old Ratt tune, "Round and Round." Pretty sure the lowest note is a D# or Eb and it looks like the bassist is using a detuned 4string. (That's what the tabs I have looked at indicate as well). If I were playing this song in a cover band, it would be more convenient to play it on a B string than detuning for one song.
Ultimately it doesn't matter what I think. If you think four strings is enough, then it's your choice and you need to accept and work around the consequences regardless of how large or small.