Having the press recharge 24 hours after you last press removes much of the strategy. You’re heavily incentivized to press the button ASAP, because if the game extends past 24 hours, you get more presses that way. A better method would have been for it to either recharge on a fixed schedule (e.g. 24 hours after the game began), or perhaps to have some special rule such as having the recharge time be inversely proportional to how long you wait to press it (such that the less time on the clock, the faster your press recharges). The latter also definitely influences strategy, but having the rule change from game to game at least changes that strategy.