I know its cheaper to buy an internal hard drive of 2 tb then it is an external hard drive of 2 tb, but why is it not recommended to back up to an internal hard drive? Obviously I wouldn't keep it in my computer because I wouldn't want it to get fried, but if I would just slide it into one of the hard drive bays in the front of my computer, back up my data, turn off my computer, remove it and put it somewhere safe, what's wrong with that?
I have never heard this before. I know it is not best practice to save important data to the same partition as a Windows OS, and when you buy a computer the hard drive only has 1 usable partition, the OS partition. So you add a partition, or an extra disk and keep data on it. Internal drives are better IMHO because there's no chance to pick it up and try to walk away while its still spinning down. I guess it depends on if you are going to make 1 copy and store it forever, or make weekly backups.
can't you just back your stuff on the internal hard drive, remove it from your system, and when you want to back up again just format the drive and back up everything again?
You can do that if you want. As DDp said, its a couple extra steps and a bit of work but will work just fine.