I can think of many reasons why a person might take a measurement that way, but it would have to be called unusual.
Say you used a dual channel programme, say REW, but with only one channel. You are able to set the gate by the beginning of the impulse, of course then you have to set the offset manually. However converting what you have there to minimum phase may cause further unnecessary changes, I can't see the benefit.
It might be useful if you inherited a set of measurements to model with and the start marker was sufficiently advanced from the impulse that it induced a lot of phase wrap. Now of course software doesn't care but visually this can be perturbing.
I seem to use a lot of these. Since you probably use a bunch of 1/8" stereo to RCA cables, you can just join them.cable
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In this case you would want to adjust the delay (the start), not the phase.It might be useful if you inherited a set of measurements to model with and the start marker was sufficiently advanced from the impulse that it induced a lot of phase wrap. Now of course software doesn't care but visually this can be perturbing.