Sure, but you still need an explanation for what would have to be reversion to ancestral forms of an italic script.

There would have been a lot of refugees from the Punic disasters, and staying a long way from Roman centers would favor survival.

Being the only literate group in a wide area would explain the surrounding majority's adoption of a non-standard script, otherwise a mystery. Use of the script could be confined to ephemera indefinitely long before a change that led to its use to inscribe durable material, so a gap, while inconvenient for historians, is hardly disposative.