Tightening lug nuts with a torque wrench (to the proper spec, which varies with the make and model) is the textbook ideal. If it’s done properly*, retorquing is not necessary. Tire shops often have relatively unskilled personnel, so they have policies to minimize their exposure to lawsuits.
Tightening by hand without a torque wrench works fine on steel wheels when done by someone with sufficient strength and a decent feel for it. Alloy wheels are touchier. They can be properly hand-tightened by someone with a really good feel, normally developed through years of experience, but even so the careful professionals will use a torque wrench on them.
Tightening with an impact wrench is often problematic, mainly from overtightening because too many people adjust the wrench to maximum power and wale away. A properly adjusted impact wrench, used intelligently, works fine on steel wheels. Not so on alloy wheels, even when using torque-limiting sockets. Using an impact wrench to tighten alloy wheels is taking a significant risk, and careful professionals will use a torque wrench instead.
If you have steel wheels, I’d suggest having a friend with sufficient strength and experience check it for you. I don’t see a compelling reason to have it done by a pro and/or with a torque wrench. If, however, you have alloy wheels, I’d have them retightened** by a pro with a torque wrench.
*Turning the wrench too quickly or too slowly will give a false torque reading.
**By which I mean loosen at least 1/4 turn (so they’re clearly too loose) and then tighten with the torque wrench. The torque wrench is only accurate in indicating the torque for a fastener that is turning at the time. If someone puts a torque wrench on it and proceeds to tighten it without loosening it first, or claims the wrench will measure how tight it is, LEAVE and find someone who knows how to use a torque wrench properly.