How about the obvious solution to all timing attacks of sending a network response after a timer set to 2^K milliseconds expires rather than when the data is re

How about the obvious solution to all timing attacks of sending a network response after a timer set to 2^K milliseconds expires rather than when the data is ready? (with K adaptively incremented and decremented only rarely, outliers managed by starting the timer again so that the time is rounded up to 2^K) This way, the only timing signal available would be which requests take an outlier amount of time, and I doubt that's enough to break anything unless you can remotely cause the peer to hit slow disks or make network requests depending on secret data (which is a far more explicit programming choice than CPU timing differences).