https://www.biblegateway.com/quicksearch/?quicksearch=Nazareth&qs_version=YLT
“Nazareth” occurs 18 times in Young’s literal translation and 12 times in a 1550 Stephanus Greek version of the Bible, so I find it hard to imagine that the town would not have existed at that time. Considering how many religious letters we have, even outside the Bible, from that time, only a fool could believe no one would have noticed a major factual error, such as central reference to a town that did not exist, in the first two centuries of Christianity.
So yes, it is VERY important to disprove claims Nazareth never existed. If not for those who believe, then for those led astray - "The truth shall set [them] free."