No, of course not, they can be both. I'm not really sure of 'Console-like' as a definition when Zelda LA is over 20 years old. LBW is also similar to LA and MC, are they both 'console-like games' too? How about Animal Crossing? Id say that 2D Zelda games and AC work just fine on either, the relatively simple visuals help a lot. Just because LTTP is the template for most 2D Zeldas, and it appeared on a console, doesn't mean that the 2D Zelda template is synonymous with 'console-like'. As other examples, I wouldn't say that Persona 4G or Monster Hunter are particularly 'console-like' games just for originating on consoles either, not when the portables have been knocking out awesome jrpgs and hunting games for a while now. Often, as machines increase in power, what was once only possible on a console becomes easily doable on a portable.
Very few people outside of Japan started out playing Fire Emblem on anything but portables, and it works great on them with being able to save after any move. Same goes for Advance Wars, both are far more popular (and just as good) as handheld games than console ones. Games dont need to be divided up into 'this is or is not suited to portables', not when there are so many old PS and VC games that have been granted a new lease of life on the portables. Some games work fine on both.
Hmm, alright, neither do I, but there's a bit of a difference between Nintendo assigning a c-tier IP like Yoshi to a b-team and Sony doing the same with big hitters like Killzone and Uncharted though. But yes, on a case-by-case basis it doesn't apply to them all, just some of the more prominent ones.
Perhaps this isnt the thread for discussing the meaning of 'console-like' either, but ill happily continue elsewhere if you prefer. I do see where youre coming from on this, and suspect we just differ on perception and semantics rather than anything really tangible.