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Depending on geometry, they may be just the cheapest
possible resistor-like element (here you'd see very long
L, near minimum W). Or sometimes, you just want a
"diode" that is not pinned to one rail or the other, at
one end or the other (well diode, not too useful except
for one side of an ESD clamp).
I don't work on stuff that's that cost sensitive so I will
use a process with a richer palette and whatever
element does the job -best-, not cheapest. But other
folks have fewer options, and you get to ride the horse
(or donkey) you're on.
The main advantage of a diode-connected transistor IMHO is the assured operation in saturation mode (VDS > VDSsat , s. the PDF below), so guaranteeing a decently large dynamic resistance as a load. View attachment diode-connection.pdf
... sometimes, you just want a "diode" that is not pinned to one rail or the other,
at one end or the other (well diode, not too useful except for one side of an ESD clamp).
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