How...
...is supposed to obtain the exclusive regional Pokemons without cheating or travelling all the continents?
Will never be able to get them if so...
Answers
Trading.
Doesn't exist yet, and when/if it comes, Niantic has already strongly implied it will require traders being in near proximity to one another.
Traveling,
OP specifically said without traveling the continents. In any case, the required traveling is not even close to being feasible for the overwhelmingly vast majority of Pokemon Go players.
Most of them suck anyway.
That has nothing to do with wanting to collect them. Many play Pokemon Go for just that purpose. I play it for both the collecting and battling aspects, so I am extremely annoyed at being excluded from reasonable access to even a few Pokemon.
If you can travel then do it. If not and you have someone where the exclusives are and trust them, you can have them log into your account and catch one for you.
Most regionals are terrible except for Heracross.
This summer I hope to make my way down to Miami and get at least 2 good Heracross and Corsala of both genders.