Consider Akkadian bētu vs. Hebrew bayit (בַּיִת) (meaning "house") and Akkadian daltu vs. Hebrew delet (דֶּלֶת) (meaning "door"). Are these endings known outside of Akkadian? If so, when did they disappear? Would they have been present in the language(s) of the Proto-Sinaitic inscriptions?
That Akkadian word-final -u is the Nominative case ending, the other case endings being -a for Accusative and -i for Genitive. Thus, the case forms of the noun bētu 'house' are:
Exactly the same case endings are still present in Literary Arabic (Modern Standard Arabic), although in most spoken Arabic dialects they are lost. The declension of the Arabic noun بَيْتُ (baytu) 'house', in the Construct state where no other suffix follows the case vowel:
Nom.: بَيْتُ (baytu)
Acc.: بَيْتَ (bayta)
Gen.: بَيْتِ (bayti)
As for Hebrew, it has no noun case category whatsoever, hence the absence of the case endings. Hebrew is a Northwest Semitic language. Case endings are found in Northwest Semitic languages in the second millennium BCE, but disappear almost totally afterwards.
So we can see that originally all the Semitic languages used to have case, but the tendency is to get rid of it, which was done in Hebrew first (no cases already in Biblical Hebrew), Arabic dialects lost it after the 7th century. Ge'ez, a dead liturgical South Semitic language (Arabic is also a South Semitic language) has (had) just two cases — unmarked Nominative, ቤት (bet) 'house', and Accusative with the suffix -a, ቤተ (beta), which is the same Accusative suffix as in Akkadian and Arabic.
As for the Proto-Sinaitic, it is definitely problematic to speak about vowels in Semitic consonantal alphabets.
* Sáenz-Badillos, Angel (1993). A History of the Hebrew Language. Cambridge University Press. Pages 36–38,43–44,47–50.