The neighbor wouldn't be the tyrannical one. And, there's better solutions - put the liability for the tree on the person whose property it's on. That's a fair assignment of responsibility. I do think it would be tyrannical for the government to declare that all trees must be removed if they meet certain criteria.
Going back to the tree example, if a tree were to fall on the house, even if all the repairs were paid for by the tree owner, the loss in time and inconvenience will not be offset. There is also the chance that something personal is damaged and no amount of money can replace it. It is better if the tree never falls on the house in the first place.
This sounds like the usual libertarian answer to things like "eliminate government food safety inspection"; the idea being that the market would eventually reflect that some restaurants regularly sicken people and would then go out of business. Why is it better to let people be sickened, even if they can later sue, than put some stops up on risky behavior in the first place?
For both tree hazards and food safety, it's not a surprise when something is risky, even if you can't predict exactly when someone will have their house smashed by a falling tree. Why wait for the damage to be done?
Consequentialist reason: you don't put barriers and friction in front of (e.g.) biotech and drug innovation. See the pandemic for this (FDA has killed approximately a million people alone by preventing covid vaccines from being available in the market sooner).
Deontological reason: you don't have the right to tell people what they can and can't do with their own bodies (w.r.t. products they want to consume, at their own risk, etc).
There's also regulatory capture, which reliably and predictably occurs in mixed economies (see e.g. public choice economics).
This does not seem like a reasonable conclusion.
In a counter-factual where (presumably) the FDA doesn’t regulate much, we don’t have any idea how many harmful drugs consumers would have been exposed to and the damage this would result in.
Nor do we know how many folks would have died of Covid after believing they were protected by whatever ineffective drugs or vaccines.
Nor do we know how many more people would refuse to take effective vaccines due to lack of confidence in them, which is a huge problem even with the current level of vetting.
Tree falls on house, tree owner doesn't want to pay their liability, what happens?