That's my preference. I do any backups of new files to a separate external drive as soon as I'm done with them, so I have no use for Time Machine myself (25+ years of doing manual backups is a hard habit to break 😉 ). I also have no desire to set aside terabytes of disk space for TM I could use for something else.
You could/should break up the external drive into two partitions. One being large enough to backup the main drive containing the OS and your apps, and the other partition for all of the documents you create, downloaded apps you purchased, etc. Essentially, anything that isn't part of the OS or your apps on the second partition. At least, that the way I prefer to do it.
You then not only have a clone of the main drive you can keep updated to match the main drive with SuperDuper! (much faster with the paid version), but you can also boot to it at any time and clone it back, or as an emergency boot drive to try and repair the main drive with any utilities you may purchase, such as DiskWarrior.
nor is there a partition for the OS in case I need to restore to factory default.
For a Mac that came with Lion, it's there, but hidden.
Let's say that if I ever needed to restore to factory default, how would I go about doing so, provided that I did not use TM or SuperDuper to make a copy of my OS?
You restart and hold down Command+R to boot to the hidden restore partition. Your options are rather limited that way though in how you can restore the main drive. There's also the dumb part that if the drive fails, your ability to restore, and your copy of Lion are also gone. Much better to use SuperDuper! or Carbon Copy Cloner to create a clone of the main drive on an independent drive.