Hebrew is the national language of Israel. It's still spoken. Latin is a dead language. I'm not knocking the idea of a church service in Latin, I simply don't understand it.
Latin is still spoken as French, Italian, and Spanish. Israeli Hebrew is different from Synagogue Hebrew as I am told. In any case the official language of Vatican City is Latin.
Hebrew was "reconstructed" in the early Zionist period, before the establishment of the State of Israel, after being effectively "dead" for centuries. It's a fascinating story ... I wish I remembered where I read it.
Hebrew remained the language of worship and of study for Jews during the 2000 years in which it was not a spoken language in the required sense. In fact, I believe many very Orthodox Jews were against its revival as a spoken language. The so-called Jewish Enlightment of the 19th century foresaw a revival of the Jewish state but many did not want Hebrew to be its language (some thought it too barbaric, and preferred -- ironically enough -- German).