Yes, if our souls leave the body and remain in this universe, then we may be able to measure this process, however, what if they don't interact with this universe? Also, how do we know that we would be able to measure or identify this process? We don't know that for sure at all. Just because it cannot be observed or measured, doesn't mean that it doesn't exist.
You say that unless we have evidence for human souls, then we shouldn't give any consideration to their existence ... well I can say that unless you are able to prove that human souls don't exist, then we must assume that they may exist.
This argument just circles ... my point, however, is that we must admit there is a 'good' possibility that we do have souls. As this cannot be proven true or false, there is an equal chance that souls do and don't exist.
It is important to remember that just because something is not visible, doesn't mean that it doesn't exist.