It depends what you mean by 'serviced'. All cars need regular checks and oil changes. The frequency of such checks is to a large extent dependent upon mileage. If older than three years, the checks of roadworthiness are done at the MoT test. If you have only done 2000 miles since the last 'service', which presumably included an oil change, all you need do is check the tyre pressures and the levels of the various fluids (brake, hydraulic, coolant, engine oil and windscreen washer) as presumably mentioned in the handbook. If enthusiastic, you might like to apply a little grease to the door hinges and the brake pipes.

The dogma of the 'annual service' is a licence for the garage trade to print money. They make a fortune from unnecessary fluid replacement and early replacement of items with thousands of miles of wear left, e.g. drive belts and braking components. A small percentage of cars are actually damaged by mechanics' carelessness when performing these tasks.

For the last 40 years I have never subjected any of our family cars to a 'service', preferring to do it myself. For the last 30yrs we have had a minimum of three cars, maximum five. It would probably have cost tens of thousands of pounds if they'd all had an annual garage 'service'.

The big difference is that if it is under warranty it makes sense to have it serviced. If it is an older car doing 2000 miles/year, waiting six months for the service will most likely not be an issue.

It depends - some older cars (and I don't mean that old [1980s and older old]) need oil and filter changes, checking the brakes, battery, etc even when doing low mileages, because the likelihood is that this mileage is mostly made up of short trips from cold, whereby the car doesn't get warmed up and that puts more stress on certain parts as mentioned on other threads.

Not doing so (not necessarily on all cars of that age and older) may be fine, but if delaying resulted in the car failing, whether temporarily (and thus being of some inconvenience as a minimum, or stopping a vital usage [e.g. shopping trips or to the doctor]) or permanently (unlucky), the result could be quite severe, perhaps leading to far high costs in having a repair or even to have to buy a replacement car.

As Avant says, I'd check out the garage/dealer to prove to the OP that they do provide the proper sanitising regime after explaining the situation and go from there, perhps using another outfit if necessary. I personally wouldn't delay, and certainly not if the car were still under warranty.

As has been said, the garage is under a legal obligation to provide such a service when working on the car. Whether they actually carry it out is another matter. Hopefully they are trustworthy and competent.