I don't know if anyone who wasn't around and watching cricket seriously in the 80s really has an idea about how big the fear was (out here at least, and I think in England too) that cricket was going to develop into a purely pace-based game, because the Windies at that time, and Australia to a large extent before them, had dominated with almost exclusively pace attacks.
There was serious talk among people who'd been watching and commentating on the game for a long time that the ICC would need to do things like mandate overs to be bowled by spin or even lengthen pitches to reduce the effectiveness of all out pace attacks, mostly because the West Indies were so damn good at it (will leave the motivations for that attitude aside).
It sounds stupid in hindsight because the two attacks which were based on all out pace were so good because they just had great bowlers, but it was genuinely seen as a worry by a number of pundits back then. Basically once they brought in mandatory over rates the issue sort of died away, but it had been a concern, so when Warne came along he was seen by some of those same pundits as a bit of a saviour of traditional cricket. It's probably no coincidence that one of the blokes who was most worried about the "death" of spin bowling was Bill O'Reilly himself, who was one of the leading cricket journos in the country almost right up til his death in late 1992.
It certainly ignores that there were other practitioners of leg spin around, but I think that context was no small part of Warne's mystique here, where we'd had the West Indies virtually every two years come over and pummel us with their quicks. There was a real feeling in the 80s that there was no answer to them or to the all pace attack. It's no excuse for Berry's hyperbole in this instance, but that was the context of the times.