Helping people with computers... one answer at a time.
Even if you use your computer as nothing more than a gateway to the internet it's likely that you still need to take care to back up important data.
Correct me if I am wrong, but I do not think I need to back-up because all I use my machine for is internet browsing, e-mail, YouTube videos, and a foreign language subscription online. I have the hard copy of Windows XP if I need to reformat and reinstall. I purposely use and run it leanly so I don't have to back-up.
You need to back up.
Your approach is a fine one, and you likely don't absolutely need to back up everything that I might otherwise suggest, but I still think you need to back up.
In fact, I hear often from people in your position who are very sorry that they did not.
Let's first look at what's stored on your PC.
Certainly, if you're ready to simply reinstall Windows when disaster strikes, that actually removes a fair amount of what you might otherwise need to backup. Certainly, you'll lose all your installed programs, and any settings and customizations, but given how lean you appear to be running that may not be a big issue. Reinstalling and reconfiguring what you do need might not be that much work.
On the other hand, restoring from a backup could be a lot less work.
But that's really a matter of choice.
You mention "email", which could be stored on your machine or on the web. If it's on the machine in a desktop email program like Outlook, Thunderbird, Windows Live Mail or others, then you absolutely need to back up or you risk losing it all.
In fact, that's rule number one: if it's on your PC, and you don't want to lose it, you must back it up.
If you don't care if it all disappears (and you're certain about this), then by all means - skip this backup.
Now, let's talk about the stuff that's not stored on your PC.
Rule number two boils down to this: if it's not on your PC, and you don't want to lose it, you must back it up.
Once again, email as the example: if your online web-based email account disappeared, was suddenly empty or simply became inaccessible, what would you do?
Would you care?
If you would care, then you should be backing it up to your PC, to another account, or to somewhere. Back it up so that when something happens to it you'll still have all, or the majority, of your data back.
This applies to anything you store online. Photos, videos, email ... anything that you store online could be lost. No, not typically by the service's own hardware failing, but more commonly by account theft or loss.
If you don't have a backup, that data is gone. Forever.
So please, think carefully about what you might lose before you decide you don't need a backup.