Many ADCs are now built on technologies that are not that good for precision
references - lacking control of the diode or BJT attributes, lacking stable and
well controlled resistors and so on.
Old-school outfits like ADI and LTC own and control specialized processes that
enable reference art unavailable to mere mortals. And your low-cost CMOS flow
that people like to use, doesn't give much of a damn about diodes, which are
supposed to be tied off and inactive more or less. Yes, you could use them.
Yes, you could model them better and maybe do a 10-bit job. Until somebody
tweaks a knob and your critical yet "non-valued" core device shifts its TC or
Vf by more than 0.1%, and you get to participate in an unscheduled redesign.