Yes, you’re correct. If something is out of kilter due to wear or damage (caster/camber) that is affecting toe then it should be noticeable when the alignment is checked.
It’s the responsibility of the alignment tech to inform the car owner (directly or indirectly through a service writer) of a problem. It’s then a matter of repairing any damage or bringing it into alignment as closely as possible if the customer does not want a repair.
Recentering the steering wheel should be part of the alignment process. If they’re not doing the above then they’re not doing the job properly.
I mention the damage scenario because there is no reason for a steering wheel to be off-center. (assuming that the alignment was never touched previously and the OP just happened to notice one day that it was off)
In this case it could be that a hard curb strike, etc. could have tweaked something (usually a control arm) and this is the cause of the off-center st. wheel.