Why does turning it off and on again actually fix so many things?
Every program keeps a pile of temporary stuff in memory while it runs, like open connections, half finished tasks and little notes to itself. Ideally it cleans that up as it goes. In practice a lot of software has small bugs where something never gets cleaned up, or two parts end up waiting on each other forever. Over days or weeks the pile grows and things get slow or stuck.
Restarting throws all of that away and starts from a known clean state. That's why it works on so many different things. The bug is still there, you've just reset the clock on it.
Routers are the classic example. A restart makes the router reconnect to your provider from scratch and clears the tables it keeps about every device and connection, which can get messy after weeks of running.
One odd detail on Windows, Shut down and Restart aren't the same. With Fast Startup on, which is the default on most PCs, Shut down saves part of the system to disk so it boots faster, so some of the stuck state can survive. Restart does the full reset. If support tells you to restart, actually click Restart.
Which device in your home needs restarting the most? And did anything ever fix it for good?