Perplexity explicitly recommends allowing PerplexityBot, because it powers the citations Perplexity shows in answers. It is a search crawler, not a training crawler.
Pair it with Perplexity-User, the agent that fetches a page live when a user's query requires it. PerplexityBot respects robots.txt; Perplexity-User, being user-initiated, generally does not.