In your example of 'an investor who waits like that is going to end up paying a much higher price', the visionary investors who said yes to the convertible note will get a very similar price (20% discount?) for taking all that risk.
Put yourself in an investors shoes: Which round would you want to invest in? Wait and see all the progress and pay 20% more or invest early and in a great scenario pay 20% less or in a worse case scenario see it go nowhere?