I think Koth's ultimate and -1 should refer to "mountain cards" just as Mountains, because Farseek just says "search for a Mountain, Plains, Island, or Swamp". The ultimate should be more like 'You get an emblem with "Permanents you control are basic Mountains in addition to their other types" and "Cards in your hand are basic Mountains in addition to their other types". This would prevent you from giving someone else the emblem (locks them down, keeps them from doing things other than playing Mountains) and from making you unable to do anything, because the cards aren't creatures or enchantments or whatever, just... Mountains. The mountains have to be basic because a "mountain card" could be anything, it could be a Sacred Foundry or a Taiga... Who knows!

EDIT: It does say "cards" on it. Well, the ultimate probably should be basic Mountains because it could be any mountain if it was a mountain card.

Actually, when I conceived this card, I started with them emblem, the whole point of which is to lock someone down. The omission of "in addition to their other types" is quite on purpose. Admittedly, it's quite cruel and should be edited to something nicer. Perhaps something that changes things into Mountains temporarily, like a tap ability added to your Mountains as seen on the original Koth.
Adding the Basic supertype is not necessary. Pretty much the only thing it would do, in fact, would be to save the permanents from nonbasic land hate. Cards turned into Mountain land cards aren't Taiga, they're Mountains.

Taiga is a Forest Mountain, so it's a mountain card. But yeah. An ultimate that locks someone down with literally no way to get out of it is brutal, and even if it takes 5 turns to get to it this would destroy a creatureless deck.

­Taiga is, in some sense, a "Mountain card," but you can't claim something is a Taiga or a Volcanic Island because it's a Mountain card.