If you dont want n'importe qui (a.k.a. everybody) to see you power or heart rate value of your public Strava activities, just give the log file a nice scrub with sed.
Removing power from TCX:
sed -i -E "/^ *<Watts>[0-9]*<\/Watts> *$/d" myride.tcx
Removing power from GPX:
sed -i -E "/^ *<power>[0-9]*<\/power> *$/d" myride.gpx
If in doubt, omit the -i
flag to inspect the actual output on stdout without having sed changing the file content.