MOTM

Theoretically you could patch a Vocoder together from standard synthesizer modules.
However, to get a similar "quality" (pun intended, but filter Q is not the whole story
here) as one of the big commercial vocoders, you'd need a lot of modules.
There are VCAs and Envelope followers needed, but let's just look at the filters
for now, as the original question was about using "standard" BP filters.

A typical BPF (like the Emu UAF, Oberheim SEM filter in BPF mode, and many
many similar filters) are two pole designs. For a good vocoder filter (a single
vocoder BPF!) you'd connect 3 such filters in series, two of them with the
same Q factor, the 3rd with a different Q, and center frequencies spread such
that the "middle" filter is halfway between the "outer" filters on a log frequency
scale. Two such blocks are needed for analysis and synthesis of one channel,
and 20 channels were a good choice for the "classic" Sennheiser vocoder.

Makes ... 3 x 2 x 20 = 120 BP filters.

The big Synton had 4 partial filters per block, but I don't remember if it had 
20 or 22 channels. Let's be conservative and calculate 20, makes
160 BP filters.

All right, the Synton's partial filters were much less demanding than the Sennheiser's,
so they used 4 instead of 3 to get comparable results. And generally you don't
need VC filters, so it's a lot easier anyway. But you still have to trim them,
which is a major pain.

On the other end of the vintage vocoder range, the Paia Vocoder has 8 channels
with 2pole filters, makes 2 x 8 = 16 filters.

Not to say that the filters are all that matters (there's a lot more), but this may
show why vocoders are normally not built from standard synth modules, and
in case they are, people start with fixed filter banks and not with BP VCFs.

JH.