What can be done to mitigate risk when buying a very old home?
It seems there are a handful of steps you could take:


Make sure you understand typical protections built into the home buying process in the US. Generally, the things that can be major health hazards (radon, lead paint, asbestos) can or should be handled as part of the purchase. At the least, if you have a bank involved to write you a mortgage, they will almost certainly require these items to be tested for and mitigated.
Make sure you understand the renovations that already happened, if possible. How did the prior owner make decisions about what to do? Were they just concerned with cosmetics, or were there updates made to the home's infrastructure as well?
Make sure you understand your home inspector's process. Home inspectors are licensed by state in the US and are essentially required to follow standards on what they inspect and how they report their findings. That said, there's a lot of variability (as with any skilled trade) so it pays to research before choosing an inspector, and then make sure you're present during the inspection and understand what they're checking and why.
Have a trusted general contractor do a separate inspection based on providing an estimate to correct issues the home inspector finds. Be present for this inspection and ask them if they see anything else. Generally, contractors won't want to literally play the role of inspector, but if you have a friendly relationship with a contractor who is willing to walk through the house with you, that can be valuable.
Have a specialized pest inspector do a pest inspection. Old homes can be easy targets for rats, ants, and other pests that can do major damage.
Take out a third party home warranty. Many people would put these one step above "snake oil" in terms of the value they provide, but if your ultimate goal is elimination of risk, that's what these policies are for. That said, taking out such a policy on an old home is going to be a pricey affair.
If the home was built in an identifiable style and time frame in an area with lots of similar homes from the same time frame, try community-sourcing feedback (via social media community groups, or asking people you know in the community, or other means you have available) on what other local homeowners have had to deal with. Maybe all these homes have similar roofs that tend to fail in a certain way, or none of them had insulation in the walls, or the wiring or plumbing has a certain typical problem, or whatever.


As a frame challenge, the uncertainty you're expressing may be a good reason to purchase a new(er) home that may still be under a builder's warranty. Or, accept that the constant need for work is part of the "charm" of owning an older home.