It was a kind of nationalist affectation, to proclaim the ancestral, pre-Babylonian-exile, Israelite origins of the newly-independent Hasmonean state—a bit like the motto of the British Royal Family (Dieu et mon droit – ‘God and my right’) is in French, harking back to its Norman origins.
Modern Israel, by the way, does much the same: the Old Hebrew script is used on the modern sheqel coin (bottom left):
The difference is, in Hasmonean times, people knew what the Old Hebrew text said, whereas 99.9% of modern Israelis haven’t a clue: most people assume it says ‘sheqel’, but in fact, it spells Yehud, which ironically is not Hebrew, but the Persian name for its Judean province, dating back to the sixth century BCE, when Persia had just conquered the Babylonian empire, and allowed all exiled nations (the Judeans included) to return to their ancestral homes.
Before the invention of printing, the ‘look’ of a script was determined by those in charge of producing large amounts of text—the professional scribes.
When Judeans first adopted the Assyrian version of the Canaanite script as their new script, some time in the 6th centuring BCE, the characters looked like this (pardon the letter order, which is left-to-right order, instead of right-to-left):
For starters, there is no historical evidence for the existence of Moses as a historical figure—i.e., a Hebrew raised as an Egyptian prince who flees into exile then returns to lead the Hebrews out of Egypt.
Secondly, the Exodus story is most likely an embellishment of the forced exodus of a quarter of a million Canaanites from northern Egypt at the end of the Middle Kingdom period in 1550 BCE, which marks the beginning of the New Kingdom period. Even if they had a charismatic leader who might serve as the basis for Moses, casual but clearly assured graffiti inscriptions in a well-defined Canaanite/Old Hebrew script on statues in the western Sinai at that time support the evidence of Canaanites indicate that by this time, even ordinary folk (probably teenage boys, or young men) were literate in that script—which indicates that the script was invented a considerable time before that.
They don’t actually have the same sound—or at least, they didn’t use to, in pre-Exile times. The tet is supposed to be pharyngealized (pronounced from the throat), while tav is not (some even speculate that tav may even have been pronounced like the English /th/).
However, in recognition of the fact that they are similar, however, when the Canaanites invented the alphabet using simplified versions of Egyptian hieroglyphs, they made tet a derivative of the tav in its form. Tav in the form of an x- or “+”-like sign, as can be seen here in a grafitti inscription made on an Egyptian statue in the Sinai ca. 1550 BCE:
As Aaron Christianson has pointed out, script and language are not the same thing: the Palaeo-Hebrew script is one thing, and the language was another—just as the Roman script is distinct from, say, the English or French or German language.