"Perfect centered by under laying spider". Is it really that easy?
I'd say no.
Of course, you can get lucky... or you could get unlucky.
I have seen several cases of both...
The spider only holds the cone (and with that the outer end of the voice coil) at one point.
The surround holds the other end - the end farthest from the voice coil.
The inner end of the voice coil is not supported.
The spider is rarely touched when doing a refoam job, leaving the placement of the surround responsible for a perfect axial movement of the voice coil in relation to the magnet pole piece.
Sellers of new surrounds often seem to play the replacement job down, refraining from showing the shim'ing process and/or telling/showing what to do when things don't work out right - thereby encouraging more DIY-buyers to try their luck.
Martin