How I see it is, if 95% of the current supply is already accounted for, then the newly minted coins are the only new supply entering the market, in smaller accounts. Other than the grayscale and confiscated coins being released (which will run out soon). It'll be just the newly mined coins and whatever is on the exchanges that's left to fight over. The demand from other players such as retail, sovereign funds, governments and others who haven't even entered the market yet should drive the price higher as they try and grab what's left of the dwindling supply.

They'll hope that we cave in and sell.

The supply shock does significantly diminish each halving. In 12 years, the block reward will be less than 1 Bitcoin. At that point 99% will have been mined and miners will make the lions share on tx fees instead of block rewards.