Aren't you just saying that if you have a nonstationary phenomenon, trying to measure the transient by measuring forever is a bad idea?

(1) If the effect persists and you can collect an unbounded number of samples, do it for as long as you like. Time is a nuisance variable anyway; it only impacts the result by impacting the sample size.

(2) If the effect persists but you cannot collect an unbounded number of samples because your opportunities go to zero too quickly as time goes to infinity, there's no point waiting once the rate gets too low.

(3) Only if the effect does not last should you time-limit to avoid dilution (either with a threshold, like you do, or by having a test statistic that checks whether the greatest observed deviation is expected by chance).