Crank sensor could be damaged but still work, and yes it does control spark and fuel injector timing, without it generating a signal you would have no spark and no fuel injectors, so a no start.
If it wasn't seated correctly to get #1 TDC at the correct time then spark timing could be off causing loss of power.
If you don't trust the shop mechanics then don't use that shop next time, but if you are just guessing that they are padding the bill then I would believe what they say.
I have a business that does similar work, not auto/truck work through, when I have to service something I often have to replace more than just the broken part, reason is that I see that something else was effected by one part breaking so if I just fix that one part I know client will have another problem shortly.
I don't want the reputation of repeated service all the time, it looks like I can't fix the problem.
Clients keep using me because things get fixed and stay fixed.
Most auto shops are the same, and why they usually use more expensive OEM parts, it is too expensive to use 3rd party parts in warranty repair cost and reputation.
And fixing a problem when you know a related part could fail is also bad for business.