Some games are simple enough to translate onto the handheld systems.
Others Require a decent size screen.

I decided to do a completionist run on M.G.S. Peace Walker.
I Finished this games story mode before I played M.G.S.3. (Internet Spoiled too much for me to play the games in proper order. Besides. I like waltzing into a mystery with questions to be answered before I dive into stories. For some reason it felt right.)
But After M.G.S.3 I decided to fully complete the thing.
I have not checked the on-line help for tips and tricks yet to get my full 100% yet but...

How did anyone read the text boxes on a handheld screen?
Half the collectable items would be a chore on the eyes to even spot.
Granted I am playing the H.D. console version but I can barely read this stuff on a big screen T.V.

Come to think of it.
Some of the G.B.A. games I have graced on this site and the D.S. games I own make me wonder.
(Mega Man X Zero 1-3, Tokyo Beat Down.)

So, list a game that should have been on the console instead of a handheld.
Good Luck.
Peace.

Well, the one I'll name is on a console, but really doesn't deserve to be handheld. Get ready.

Well, CoD for the DS. Seriously? It's stupid. You can barely play correctly, since the DS has limited buttons and advantages. It's crap. You'd be better off playing on the Xbox, or even the Wii. 

goodboy : I played CoD 4 on DS and really enjoyed it. The only shooter on Wii I have played was Conduit, and that game is really good.

I don't think any game "doesn't deserve" to be on handhelds, as the more consoles something is on, the better it will be.

Tails the Fox : CoD 4 was cool, I'll admit. But other than that, I found them awkward.