You need fans to distribute heat evenly across the board to ensure the stability of the measurements.
There are plenty 6.5 digit (and better) meters without a fan (like the venerable HP 34401A). It's just a matter of thermal management: how much heat the instrument produces and how the engineers decided to get rid of the heat. Actually if you watch Dave's video about the HP 3457A tear down, you'll find him saying the instrument does not have a fan because the air currents would introduce thermal gradients. You can also find good 6.5+ digit meters with a fan, though.
The two 34401As we have, one is an old HP and the other a AG version, are the ones we use the most. They are quiet, quick, stable, and precise. They've had years for the nice selected LM399s to stabilize, and probably one of the finest, if not the finest, electronics instruments ever created, stunningly good instruments that have held up amazingly well over time

All toll, we have and use seven 6 1/2 digit DMMs, 3 KS34465A, DMM6500, SDM3065X, and mentioned two 34401As (a few handhelds). Long story how all these were acquired (recently last KS34465A by accident), but some of our previous use cases demanded extreme accuracy in various parameters and results reproduced "blindly" in areas we weren't allowed to attend, so "hand off" if you will
The SDM3065X is a nice DMM, but not in the same league as these others, however it costs about 1/2 the 34465a or DMM6500, so a good value in that respect. The fan is not too bad, little louder than KS or DMM, and the general performance is OK. Would like to operate longer to help "age" the LM399 (understand it's not selected nor aged), but fan is loud enough to prevent continuous operation and we generally only operate the SDM3065X when other instruments with fans are operating.
We've thought about disabling the fan, but as others mentioned this might disrupt the calibration and introduce thermal issues, and our various instruments are stacked, which introduces other thermal effects, so haven't attempted to disable the fan.
Which brings up an interesting point about having a SDM3065X power down mode where the display & fan are off, as is most of the circuitry, but having a scavenged power mode that keeps the LM399 reference biased on to assist in "aging". Understand why Siglent doesn't use a preselected and aged LM399, too expensive for this price range DMM, but this could help the user "age" the reference without keeping everything else active, including the fan.
Anyway, just a thought.
Best,