I gave my hyundai Elite i20 for second servicing(5000 Kms) and according to user manual the service center was supposed to do tyre rotation, but the service manager told me that without doing wheel alignment and balancing they would not do tyre rotation. According to user manual wheel balancing is recommended in 2nd servicing but not important. Is it really necessary to do wheel alignment after just 5k Kms?
I would suggest balancing is necessary, alignment perhaps not, depending on your vehicle, servicing etc.
Tyres vary in consistency - tolerances are generally better for more expnsive tyres (but not all) - and wheels get chips out of them, corrode etc. So whenever you change tyres, balancing should be an automatic part of the process. If you miss it, you may expect vibration - sometimes very minimal, sometimes excessive. Removing vibration is always a good thing - it extends mechanical life.
Alignment is more subjective. I like to have mine checked once a year anyway, so I do it when I change tyres. It shouldn't really be needed, but through the year you may well hit potholes, have some big bumps and so on, all of which could slightly alter alignment. With your service schedule specifying it for the 5k service, I can only assume it is to compensate for suspension and tracking components bedding in from new.
In any case, it's worth doing if the service schedule says so, that way you can have a clean record in the service book in case of problems further down the line :-)
If you can't feel a measurable vibration especially at 50-70mph your wheels are balanced to within the spec of the seat of your pants. If you can't feel a vibration and the tires/wheels are undamaged, it's a ride quality issue, nothing else.
Balance them if you want to get the best performance out of your vehicle. It's in the service schedule to keep your car driving as well as it was designed to.
Bear in mind the service manager's decision was based on the overall condition of your vehicle, or at least had access to that information. If your tires are not ALL evenly worn or your suspension not in good shape it affects the decision of where to put the tires and whether to do other services. It even depends front wheel, rear wheel, or all-wheel drive.
Ask him for his reasoning, then call one of his techs over and ask them when the last time they balanced the wheels and aligned Mom's car was.
Of course you can rotate tires without performing a wheel alignment! A reputable alignment shop will put the car on the alignment rack and measure the alignment for free, then give you a print-out showing any mis-alignment. You will then be able to decide for yourself if the car needs an alignment.