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The power delivered to a load (of any kind) from a lossless transmission
line section, is the same as the power delivered by the source.

So it is your contention that power is not reflected at a mismatch. The wave
certainly is so the power contained in the reflected portion must be as
well.

You assertion that you have travelling forward and reflected power waves
on the transmission line runs into a problem when you try to analyse the
combination of both at a point (eg the input to the line) as power
doesn't combine vectorially.

I was not trying to analyse the combination of any wave on the line ("power"
waves, whatever they may be, or anything else), I was merely noting that you
can quantify and measure the power contained the both the forward and
reflected waves and they are real quantities.

Jeff