You're assuming that startups are more innovative than large companies, but this is only true because the market is not efficient. An "efficient" enterprise would perfectly invest in innovation.
emh doesn't mean everyone knows everything, it means the price accurately reflects available information. if an innovation was believed to be world changing, it would be worth a lot, if the belief changes, the price changes.
The economy is a faith-based construct. Prices aren't set by "information", but by faith in value - which is one of the easiest things in the world to lie about.
In EMH there is cooked in some notion of overall largely rational beliefs, and yet the shares trade hands from someone selling to someone buying - both of which feel they got a good deal worth making money from.