I've done the job of mounting, balancing & patching many times. The "properly" part is trivial. So is the cost of the equipment.
To do it properly takes only your ability to learn basic things. Ask me anything you want about how to do the job properly.
See if you can find anywhere where I'm not doing it properly at home.
The equipment pays for itself so the only real cost is the storage of it. People who have no place to mount the changer, for example, can't do it.
The main justification is whether you want to do the job or not. If you do the job, you know it's done right.
If you pay someone to do the job, it will almost always be done wrong.
But you might not care if they do some things wrong, like someone said they have to check the lug nut torque, or the air pressure, or they scratch the rim, or they don't mount the valve stems where they should have put them or they didn't use a patchplug or they ripped off your wheelcovers wrong.
Whatever they can do wrong, they will do wrong because they don't give a s*it about your car or your tires or your wheels.
They're doing it for cash. Like contract soldiers. You're doing it for yourself.
People who don't want to do it for themselves will always find a justification of why they can't or don't want to do it for themselves.
To me, having someone do it for me is like paying them to wipe my ass. But to others, it's like paying someone to clean up the toilet afterward.
The only thing different is the attitude of the person. Ask me anything you want about how to do the job properly.
It has nothing to do with can you do it or should you do it. Whether or not you want to do it is the only thing that ever matters.
It's kind of like justifying whether you should hire a landscaper or not.
If you hate trimming your roses, then you'll find reasons to hire him. If you think you need too many tools, you'll find reasons to hire him. If you are worried you'll get injured, you'll find reasons to hire him.
It's not a question of can you or should you pay someone to trim roses. It's only a question of whether or not you want to do your own trimming.
Come to think of it, trimming roses probably is more difficult than mounting and balancing passenger car and light truck tires at home.
Ask me anything you want about how to do the tire changing job properly. (I don't know anything about how to trim rosebushes so don't ask me that.)