I am not convinced that lowering the interest rate on reserves from one quarter of a percent to zero will have much of an effect on investment activity. What we need is a reason for firms to want to invest, and that will require a much improved outlook for the economy, something that could be aided by the government providing additional stimulus to aggregate demand.
What he is suggesting is that the combined elasticities of money supply and money demand are low enough that eliminating interest payments on reserves would have a negligible effect on loan demand, which in turn means that it would have a negligible effect on the money supply and on the amount of reserves held by banks.
That is a legitimate, plausible hypothesis. However, even if it is true, eliminating interest on reserves still would make sense. If monetary growth is being restrained by weak loan demand, then this eliminates the rationale for paying interest on reserves, which was to restrain the impact on the money supply of the Fed doubling its balance sheet. We might as well save taxpayers the money by eliminating the interest on reserves. From a Keynesian point of view, it would be better to use the money now being paid out as interest on reserves to cut taxes or increase spending, rather than to let it sit at banks doing nothing.