[Avodah] Ta'amai d'kra - why do we put tephillin on our weaker arm

[M Cohen via Avodah]

why do we put tephillin on our weaker arm?
(I know its bc of the drasha of yad kaiha)

But in terms of ta'amai mitzvos..

assuming the head tephillin represents shibud of our head/brain to HKBH,
and the arm tephillin represents shibud of our strength to HKBH
then arm tephillin sbe on our stronger arm

and if the arm tephillin represents shibud of our heart to HKBH
then arm tephillin s always be on our left arm (even for a lefty)

so I remain with my question - in terms of ta'amai mitzvos why do we put
tephillin on our weaker arm?

mc