It does not posses a "memory".
Possessing memory and possibility for glitch filtering are probably the most important advantages of MCU solution. Surely the MCU based solution won't be more precise, like you wrote this is simple physics, but it can be made harder to disturb and quicker to converge after a cold start.
As most people here seem to have magnitude of orders more time (and ambitions) than me for this kind of things probably my glitch filtering is not very well worked out (or primitive if you like) but nevertheless the idea is here:
There is an x (currently 4) item FIFO queue and then its average is compared to the last measurement. If it's within tolerance it's used for compensation calculation, if not then it is not used. It gets to the queue though no matter what.
One can play with tolerance and queue length (kind of an adaptive FIR filter).
Due to saved compensation value cold start is typically within 8 digits precision with TCXO just after start (although depends on aging retrace and assumes relatively stable temperature) and within 9 digits in around a minute (that is roughly the max).
With OCXO the fast start gain is not so much as OCXO warm-up is slow (my relatively quick double oven OCXO starts with roughly 330 Hz error, stability getting within 1Hz takes around 5 mins, within 1mHz yet another 5 mins) and aging retrace is also higher. So in short, after cold start mostly only aging retrace has to be compensated thus it can be made faster.
If someone does not know what is aging retrace (and many other interesting XO related stuff) I copy a link from FA2 topic here:
https://apps.dtic.mil/dtic/tr/fulltext/u2/a248503.pdfI don't know what can be the root cause for lamp disturbance (can guess from micro-volts) but what I've experienced is vibration. Even accidentally knocking something close enough can cause a short jump in the order of mHz. Analogue loop will chase it with a damped oscillation, digital can just ignore the glitch (sounds easier than done). This is where I've actually lost most of my ambitions for precision. If something is so easy to disturb, it's really not practical to use. It's fun to play with it but that's it.