When I last priced the equipment it wasn't that bad costwise. In my case though it was only worth it to get rid of the whole "dealing with tire shops" issue. A close friend owns a used car dealership and they bought the mounter and balancer. IIRC...it just needed a 240v line.
I have also lost days waiting for tire shops and alignment...as those are the only 2 things I don't do myself.
A tire machine is life changing in a good way if you have a lot of cars you're responsible for. China is starting to make mid-market ones (simple pneumatic ones that are powered bug geared to home use rather than professional like the ~$1k electric machines) for ~$400ish that I'd take seriously if I was in the market
Once you have a tire machine you'll spend more time at the tire shop (outside business hours, lol) because their trash pile will be your best source for reasonably new used tires. They sell a lot of sets of 4 when 2 would do.
definitely not easy by yourself, but the whole process (change, then alignment etc) shouldn't take a decent mechanic's shop more than a couple of hours. I've changed tires on my nearly 200k mile car several times now, and it's usually a few days for the tires to be delivered (in america the mechanic will just receive it) and a 2h appt to get the work done. I'm shocked your parent comment mentioned waiting a whole day at the mechanics'.
My friend does this at Costco, and it takes longer purely because of appt mismanagement and backup, the work itself is quick.