There have definitely been times when all I really wanted was just access to the same search term-based FAQ portal their frontline tech support had in front of them (because their online FAQ was worthless). But the majority of times I actually call tech support, it's only because the issue is something I already know can only be resolved by a human taking an active, out-of-normal-process action on their end, so all the attempts to 'divert' me to their alternative self-serve paths are just annoying wastes of time.
If they would actually empower the LLM to assess the context and initiate an out-of-flow action, like resetting the account auth in the back-end because it's gotten munged in an irreparable way or authorizing a cross-ship/refund. I highly doubt most orgs will allow LLMs to unilaterally make those decisions, so this will just be an all-new way to force customers to go through the entire diversion tree before getting through to the 'organizational node' sufficiently empowered to resolve the problem by expending carefully gated resources.
Unfortunately, since this will have no "press #" way to quickly exut, the metrics will look like "the LLM cut our live operator call load by 12%!" when in reality it'll just be reflecting customers who gave up when faced with an even higher barrier they couldn't work around, silently resolving to never do business with the company again. The VP of Customer Support will get a bonus for buffing the metrics but sales will later go down and no one will know why.