Randomness is possible.*
You just have to be really smart and really dedicated to make it happen. Serious programming chops required.
Most of the very natural looking handwriting fonts you'll find use contextual alternates and complicated ligature substitution. This actually achieves a more natural result than randomization.
Some great examples of consistent substitutions can be seen in the script fonts from by Sudtipos. Their recent release Rolling Pen is an excellent specimen.
Rolling Pen is another cup of mine that runneth over with alternates,
swashes, ligatures, and other techy perks. To explore its full
potential, please use it in a program that supports OpenType features
for advanced typography.

* History lesson
For those of you who remember the great Beowolf font from Just van Rossum and Erik van Blokland, it's back. Kind of.

Here's the story from FontFont:
FF Beowolf was born at the end of the dark and murky 1980s when Just
van Rossum and Erik van Blokland found a way to change the programming
in PostScript fonts. When printed, each point in each letter in every
word on the page would move randomly, giving the letters a shaken,
distraught appearance. Initially dubbed “RandomFont”, van Blokland and
van Rossum created three versions with increasing degrees of potential
randomness and FontShop released it as FF Beowolf, the first typeface
with a mind of its own.
The technology in FF Beowolf wasn’t what computer and printer
manufacturers had in mind for desktop publishing. So, while it worked
great (if a tad slow) through most of the 1990s, FF Beowolf was
eventually barred from performing its magic: pesky things like printer
drivers and operating systems learned to ignore the non-standard. FF
Beowolf seemed relegated to mere recollection.
But OpenType technology brought new hope, forging paths in the
typetech continuum which would eventually lead to a new generation of
RandomFonts. Each glyph in each font has ten alternates and a massive
Faustian brain to control the mayhem. Specially developed and
hellishly complex software, nearly ninety thousand glyphs, and an army
of purpose-built ’bots took days to forge the OpenType features no
ordinary type tool could have assembled.
[...] The randomness performs on screen in any application on MacOS
and Windows which supports OpenType.
a
in...sa...
might be different to in...ta...
to...ma...
to...ssa...
to...sau...
etc etc - but two identical words would look identical. Fonts also allow variants on letters that can be applied manually, which you could use to 'fix' repeated words near each other so they aren't identical on the same page (or, you could skip some ligatures). I can't remember a source for this though, think it was an interview with a handwriting font maker on MyFonts from about a year ago – user56reinstatemonica8 Jan 31 '14 at 10:33fi
and thef
is tucked over thei
and the dot on thei
is gone, then it is probably an automatic ligature replacement. – horatio Jan 31 '14 at 15:00