No
seriously this is not at all the case.
Absolutely First Nations were to varying degrees shrunk massively from pre-contact highs, there's no debate, but the loss of cultural memory, art, music, and language really only happened very recently, in the last 100 years, and was directly related to government and religious orders imposing residential schools and literal government bans on cultural activity and organization (eg. Potlatch).
This is not ancient history. The potlatch ban only came into effect in 1885 and was only removed in 1951. Residential schools were only closed in the 1970s.
You can see evidence of this in NW Coast art, where post contact, pre 1900s, there was actually a renaissance in art production and development, as superior iron tooling made it easier than ever to make art, and creation of carvings for the tourist market opened up all sorts of new economic opportunities for First Nations people.
Then in the late 1800s the government imposes literal bans on cultural activity and brings in residential schools. Enormous loss of cultural memory occurs.
By 1969 no one on Haida Gwaii had raised a totem pole in living memory, but Robert Davidson carved one and raised it. He couldn't speak Haida. No one even knew what to do at a totem raising. Luckily there were a handful of old timers that vaguely knew enough to kick start this cultural revitalization.
https://www.cbc.ca/news/canada/british-columbia/haida-totem-...
If indigenous art and culture was already dead due "inevitable" disease, then why would the government feel any need to actively try to ban it, police it and arrest indigenous people for taking part? So you can see here that no, despite population decreases, indigenous customs were quite alive and well. The destruction required a brutal government clamp down to try to snuff it out.
Potlatch ban:
https://www.ictinc.ca/the-potlatch-ban-abolishment-of-first-...
https://www.sfu.ca/brc/online_exhibits/masks-2-0/the-potlatc...