It's hard for me to really make a coherent model from the email complaints of the missing man's cousin, but it seems that she is convinced, with 20/20 hindsight, that he's missing in a particular canyon (Lady Northcote Canyon) on the basis that a report to hand (on day 8 of his excursion?) suggested that a voice may have been heard. Odd that an experienced hiker with extensive outdoor experience wouldn't carry a whistle, but ok.
The cousin states that the lost man "easily could've lost his footing and fell into ANY area where they think it’s difficult for him to have gotten to." Which I take to mean that she accepts that he could be in just about any hole anywhere within some radius of his last known position. Further, she accepts that searching the canyon in question would "need ropes and harnesses and someone with experience of mountain climbing."
She then asks, rhetorically, by way of criticism of the search effort:
If these are the most experienced and professional hikers out there, why haven't they sent a mountain climber to search that area?
Of course, they're volunteers, not professionals, for the most part. But more importantly, perhaps they haven't sent a mountain climber to search that area because they are not convinced of the reported voice, because they don't want to expose someone else to the risk of searching that canyon in the prevailing conditions, or even because there's nobody with the necessary skills available and willing to do it.
Like it or not, there is a cost and an actual risk to every phase of searching, and it is the responsibility of the person directing the search to allocate resources with a view to containing costs and minimising avoidable risk to searchers when it is judged to yield no probable benefit.
If events show that the people conducting the search made an avoidable error, or even if there is proven to have been a possible course of action which could hypothetically have located the man alive, or his remains, then that would of course be lamentable. In any case, though, the people conducting the search cannot be judged with the benefit of hindsight, but only in the light of what they knew, and whether their judgements were reasonable at the time. I see no reason to doubt they have been.