People have made, and do make delta-VT references which
act similarly. However they are subject to more influences
(and less controlled ones) than the simple diode or substrate
BJT. The BJT gain, poor as it is in a "substrate PNP" device,
helps to linearize the diode I/logV curve (you want that to
be linear on both sides of both single and N-fold diode groups'
operating current density, across the temperature range).
PN diodes can be designed so that little or none of the
forward current involves the surface interface, where the
trap density and surface recombination velocity are quite
process- and stress-variable. The junction itself is as well
controlled as the implant dose & energy (which is a process
control point that is monitored). Surface quality effects,
especially ones which bother minority carrier devices but
only affect CMOS leakage a little bit, not so much.