Centaurus, the technical logic of your argument appears sound, but choosing to have reverse available ‘just-in-case’ might be an ineffective tactical option.
As you say it takes time for the engine to spool-up, perhaps even longer for the mental decision to spool-up to recognise the need for more retardation.
From a landing safety perspective it might be more efficient (safety) to decide to use some higher level reverse as judged in the pre landing briefing based on the reported conditions, or even by SOP, and then during landing when assured of stopping, reverse can reduced to idle. Thus the suggested option of a ‘higher idle’ is moving in a safe direction.
Unfortunately many of the operational decisions are influenced by commercial efficiency, where safety aspects are deferred to late ‘tactical’ crew decisions exposing the crew to the frailties of human behaviour and performance.
Brakes may be cheaper than engine overhaul, but neither compares with the cost of an overrun.