That has not been my experience. I find all other things being equal, the pickup construction, their position and the electrical network they form impart a certain characteristic on the guitar sound.
Amps+Cabs can certainly have a more dramatic tonal change no doubt; For me however it’s still a change of that characteristic sound.
For me, all it took was a pickup change on my Carvin DC127C for me to love it again (Going from Carvins to Dimarzio Liquifire/Crunchlab combination)
Or using Bill Lawrence’s L200 set on my Carvin Bolt:
A great example of pickup differences was done by Keith Merrow