In theory it's a simple decision.
If you have dynamic content that it would be useful to display on a wide live tile then you should include one.
If you don't then you shouldn't.
i.e. Don't include a wide tile if it's just a static logo.
So why even discuss this?
Well, most of the challenges on DVLUP require inclusion of all three tile sizes.
In making this requirement they're saying to add functionality regardless of whether or not it makes sense for an app.
You may object and I think you'd be right. Microsoft agree (Sorry, I can't remember which of these videos it's in. But if you haven't watched them they're all good.)
You shouldn't add unnecessary functionality or features just for the sake of it.
But here's the catch, and the idea behind my opening paragraph.
If you care about the DVLUP challenge just add the wide tile. Ok, so no-one is ever going to pin your app with it but it will only take you seconds to create the tile image (because you'll just be creating a different size version of an asset you already have).
But won't that be a waste of time?
Yes, but you've already wasted more time thinking about whether you should do it than it will take to make the tile.
Use your time wisely. Build great apps with awesome, useful features. Don't waste your time discussing things that don't really matter.
Just include the tiles if you want the XP. But feel free to know that you know better than the person who sets the DVLUP challenges. ;)