Recently saw a pretty popular history youtuber in Taiwan who claimed in one of his episodes that the character 石, no matter used in whatever context, should and has always been read as shí [ʂɻ̩˧˥]. He claimed that reading it as dàn [tan˥˩] when 石 is used as a unit of weight has been wrong from the start, and it is only tolerated because so many people read it wrong.
I think that’s just plain wrong.
Consider characters such as 拓 /tʰuo/ and 妬 /tu/, both were said to sound the same as 石 in Shuowen Jiezi (說文解字) and other rhyme books, they both starts with dental and alveolar plosive, just like the dàn [tan˥˩] reading.
To get to 石’s many modern readings across Sinitic languages (by that I mean Taigi and Mandarin), there are three common sound changes at play. In Old Chinese, 石 is most likely pronounced as /*dAk/. The first thing that happened was the /t/ > /ts/ > /s/ > /∅/ sound change. I went over that in that previous thread in detail. Some quick examples for that sound change would be 跌 t /秩 ts /失 s and 特 t /持 ts /寺 s. So in Middle Chinese, the most common initial vowel sound of 石 became ts, such as Taigi’s tsio̍h, and that eventually became s, such as Taigi’s si̍k and Mandarin’s shí.
The second sound change was the loss of final stops resulting in au and ou diphthongs. Again, details in that thread, but basic examples would be 覺(kak > jiau), 教(kah > jiau), 角(kak > jiau), and 拓(thak > thou), 國(kok > gou), and 薄(po̍k > buo, bau), 落 (la̍k > luo, lau), 著 (tio̍h > zhuo, zhau), 酪(lo̍k > luo, lao). From -uu you can go a step further to just -u, 塑(sok > shou, shu), 獨(to̍k > tu), 度(to̍k > tu), 毒(to̍k > tu). In same rare cases you can even get a schwa, like 各(kok > kə. This sound change is what got 拓 and 妬 from /*dAk/ to /tʰuo/ /tu/.
The final sound change, is the even lesser known effect of the loss of final stops resulting in nasalization, /-p/, /-t/, /-k/, /-h/ > /-n/. Examples of this phenomenon: 厭(iap > ian), 勿(but)/吻(bún), 妲(tat)/旦(tàn), 掠(lia̍h, lio̍k, la̍k)/京(kiann). This last one is what get 石 /*dAk/ to dàn [tan˥˩].
So not only is it linguistically sound for 石 to be pronounced as dàn [tan˥˩], since the third sound change seems to be the first one to have taken place, dàn [tan˥˩] is probably the oldest pronunciation of all possible pronunciations of 石.