Why should the law care about what I do behind closed doors?

The law shouldn't care (if you are a law abiding citizen) about who you take into the bedroom as long as they are consenting adults. How many guns you own. What you eat for supper. What kind of TV shows you watch. Whether you watch porn or not.

Your speech is free. But if it causes malicious harm to someone, you can be sued.

Society sets laws announcing those actions that it deems unacceptable in polite society. If evidence appears that causes a reasonable person to suspect that illegal activity is going on, society should investigate. Of course society might find itself having to jump through hoops by adhering to constitutional law. It cannot just invade your personal space and demand to know what you're up to just because they don't like you.

The Tech Industry Said It Was "Impossible" to Create AI Based Entirely on Ethically-Sourced Data, So These Scientists Proved Them Wrong in Spectacular Fashion - futurism.com

It shouldn't to a point.

But what if you're raping little girls behind closed doors? Killing gay men? Watching child porn?

Liberty is not boundless. It does have its limits.

Are today’s baseball pitchers faster than a few years ago, or is it that radar guns have improved and get the pitch speed as it is released rather than as it reaches the plate?

You can stand on a public sidewalk and take pictures of my house. You can't walk into my house uninvited and start taking pictures.

If evidence arises that you are doing these things behind closed doors, don't you think the government has a moral obligation to investigate?

The law doesn't care about what you do behind closed doors as long as it is within the bounds of what the law allows.

Why is the concept of pumping water uphill not commonly used as a source of electricity generation, similar to pumped-hydro systems?