> The last check on power is murdering politicians in their homes?
You said murder, but there are plenty of valid reasons that the public should know who holds positions of power and where they live that don't involve violence of any kind.
Protest is an essential freedom we have and it's perfectly valid to do it outside of the homes of those we have put in power. It's also useful to have that information when investigating fraud and corruption.
I don't think there is any reason to protest outside people's personal residences. People can protest at a government building, or a public square, or somewhere intentionally disruptive that isn't implicitly aimed at intimidating a public servant. Especially given that protests can turn violent, having a mob outside a specific individual's house is reckless and can quickly escalate in the wrong way. I think it's worth noting that the people protesting won't always be people you agree with. People protest both sides of a given cause. Perhaps you think it is justified to form an intimidation mob for your cause, but would you feel the same way about the opposing side of the issue doing the same? For a civil society to flourish, I think there needs to be a common understanding that there are limits to how people should conduct themselves.
> It's also useful to have that information when investigating fraud and corruption.
This is the purview of journalists, police, and independent investigative boards. We do not need random unqualified people stalking politicians to uncover fraud. I'm not sure I've ever heard of a case where that a random nobody ended up uncovering fraud or corruption by stalking, but I have heard of dozens of cases of public servants being targeted and murdered in their homes.