Ever been to a server farm? Rows and rows of computers, hundreds of 'em. For the most part, they are only shut down for maintenance. Ever been in a mainframe computer room? Enormous "big iron" systems that fill a warehouse-size space, and might be shut down once a year for maintenance. There are literally millions of computer systems around the world that essentially never shut down. And they run far more critical missions than recording music. They manage the world's internet traffic, as well as cell phones, 911 services, monitoring oil and gas pipelines, nuclear reactors and air traffic control. They pretty much do it 24x7 with only occasional (scheduled) shutdowns.
Of course, these are climate-controlled rooms. Power conditioning, air conditioning, humidity regulation, filtered air. They're noisy because there are hundreds or thousands of fans going. Contrast that to your laptop, which has to quietly function in all kinds of environments.
Whether you need to shut your computer down or not really depends on the computer (desktop vs laptop, water-cooled vs single fan) and its environment (hot and humid vs. cool and dry, prone to bad power and lightning, conditioned power vs. sharing a circuit with leaf-blowers). Look inside your computer; is it clean or stuffed with dust bunnies? Does the CPU heatsink still allow airflow, or is it clogged with dust? Have you ever even
seen the CPU heatsink? Is the PSU intake clogged? How about the air filters on your disk drives? They have to suck in air, too.
My own practice is to shut down once a week, and vacuum the case out once a month. I'm more likely to shut a laptop completely off because heat stress is more likely in a laptop.