There are zero disadvantages in using Time Machine, I've been using it for 10 years now. It has saved me from my own stupid mistakes a few times. My wife's MacBook drive also crashed. I opened the computer up, installed a new drive, plugged in the TM backup drive, booted from the TM drive, copied absolutely everything over and she picked up exactly where she left off, nothing lost, at all.
The biggest draw back with manually copying files is the time, and space that it can take, depending on just how much data you have. Between my wife and I, we have a total of 2.4TB of music, movies and photos. Now suppose we add just a few MB's of new stuff to our libraries, which we do on a daily basis, how do we back that up, instead of the entire 2.4TB of existing stuff every time? Time Machine makes automatic incremental backups, meaning it only copies to your backup drive the changes made since your last backup. What TM also allows you to do is easily backup to more than one drive. We have 2, one of which I keep at my in-laws house. Keeping all your backups in the same place as your computer is risky. Natural disasters happen, unfortunately. When we go there for Sunday lunch I take the one drive with me and swap them in order to keep them both up to date. 2x 5TB Seagate portables that cost a paltry €110 each on Amazon, a very small price compared to the value of our data, especially the family and travel photos from the last 60 odd years.
TM setup is very intuitive and once that's done, it's practically plug and play. You can also back up other external drives to TM.