Bitcoin's inflation will be getting smaller and smaller. If this cryptocoin survive through many years it is natural to have high price like $1k because of mentioned inflation. However noone knows if it will survive so many years - goverment interventions are still an issue. They can close all the major exchanges and let BTC to die slowly 
I doubt bitcoin will hit $1k anytime soon. I know I won't pay $1k for a bitcoin.
Would you pay $100 for a bitcoin? People said they'd never pay $100 for one, when it was worth $4.
Logically this doesn't work. You can always say well it started at X and once was X. This doesn't hold any weight in how the price is determined.