I disagree, ceteris paribus the conversion associated with each channel will be about the same once you past the longest conversion window. We are not attempting to land on the moon, a high degree of precision is not required. This is cookie based analysis so there goes any degree of precision, there is more precise "user finger print" type of analysis but that gets creepy.
All other things aren't held equal in the real world. You may add a new campaign, or stop one that is currently running. You might change up the audiences or add to them. Basically any activity you would do to optimize a campaign is going to potentially change a channel's behavior. Either you limit yourself to not making those changes, or you severely slow down your decision cycles by constraining them to an amount of time based on the longest conversion window.
That may be an acceptable way to run marketing with small budgets (say under $20k/mo) since you don't have the spend volume to come to many new statistically significant insights about what is working and what is not in short timeframes, but once you get to larger budgets the method of hoping that all other variables are equal-ish is a great way to lose money on marketing. If you run substantial marketing accounts it trivial to see the differences in practice between the model you suggest and a more accurate model, you shouldn't just hand-wave away the differences.
