Information asymmetry is only valuable if you can execute on it. All of your examples are actually examples of both asymmetry and market control. HVAC, there's typically only a few legitimate licensed providers in town so they can set the price however they want. Car servicing, indie shops are always better but if you want to maintain your warranty you'll need to use a stealership which goes by a book (and it's mandatory).
I'm not convinced an LLM can help with these situations. I would suspect you're more likely to get a "screw you" price in return rather than winning a negotiation. When I shopped for a new HVAC after mine gave up the ghost after 20 years most providers were within a few hundred dollars of each other. An LLM would've been useful here for warnings ("you probably dont need ducting", "you probably don't need duct cleaning") but as for the bulk of the cost there's a monopoly and there ain't nothin you can do about it. When I got my yard worked on it was a similar story. Despite every landscaper providing offers from cheap to absurd, the ones that I could sue if they hit a gas line were all within the same price range.
These people are also very used to the "know-it-all homeowner". They're more likely to ignore you than help you because if you actually knew-it-all you'd do it yourself.
I think, rather, LLMs will be extremely useful in bill negotiation where the data is absolutely clear, you have a copy of it, and it can be analyzed in full (no asymmetry). For example, an LLM could be trained on medical billing codes and be able to analyze your bills for improperly coded procedures (very common).