Apparently palatalization of
[ж] MAY occur in cases of its phonetic gemination
[жж] due to assimilation of an adjacent phoneme of the word root. In all such cases this adjacent phoneme can alternate with
[ж] in other roots as well.
Other such words are:
дожди (rains) - which can be pronounced
[дажжи] due to assimilation of
[д] able to alternate with
[ж] in other roots as well: сад - сажать, сидеть - сижу etc.
подожди (wait!) -
[падажжи] for reason as in 1)
позже (later) -
[пожже] due to assimilation of
[з] able to alternate with
[ж] in other roots as well: лазить - лажу, возить - вожу etc.
вожжи (reins) - this is conventional spelling, which can also have the form of
возжи because its root is essentially
воз just like in the verb
возить mentioned above, so the reason for gemination
[жж] is as in 3)
4а) also sing.
вожжа - which can be pronounced as
жжёт (burns) - this is conventional spelling, where the gemination
[жж] occurs due to assimilation of the root phoneme
[г] which features in such cognates as
ожоГ and which is able to alternate with
[ж] in other roots as well: бог - божиться, могу - может, лог - ложбина, рог - рожок, друг - дружить etc.
Now the gemination
дрожжи, which is conventional spelling like
жжёт, can't be explained by reference to its root or other Russian words, because the word is unique. However it can be explained by reference to its etymology and equivalents in other Slavic languages
Происходит от праслав. *drozga, от кот. в числе прочего произошли:
ст.-слав. дрождиѩ мн. (Син. Пс.), укр. дрíжджi, дрíщi, болг. дро́ждие,
сербохорв. дро̀жда ж., словенск. drôzga «отвар солода», чешск. droždí
«дрожжи», словацк. droždie мн., польск. drożdże, в.-луж. droždźe,
Apparently it derives from the root
дрозг. Whatever the case, all
г can (as shown above) assimilate into or alternate with
ж to fashion gemination
Дажжи (дожди) и
падажжи (подожди) are different from the rest in this list in that palatalized pronunciation of
[жж] in them is the only option. Their penultimate phoneme
[д] is palatalized in the normative pronunciation due to
[и], so after its assimilation into
[ж] the palatalization is simply kept.
The other words allow for alternative pronunciation, either with or without palatalization.