Ideally the answer is yes. A repairman should service all appliances regularly, to look after them and keep them in good condition. We live in times where many appliances are proving unsafe, and even dangerous. So we definitely shouldn’t take chances (Appliance safety issues). However..
The problem with regular servicing
In a word, cost. The problem is that over the last few decades washing machine costs have come down considerably (in real terms), while at the same time the cost of getting an engineer out has gone through the roof. It’s got so ridiculous that many manufacturers have even had to abandon their normal engineer charging systems and have resorted to insurance-based schemes. If you wanted a manufacturers engineer to come and service your washing machine after 12 months it would cost over £100. You may have only paid 300 or even less to buy it.
So most washing machines are just not expensive enough to warrant investing money each year on servicing. A local engineer is likely to be a lot cheaper, but it could still cost £50 or more. The economics just don't encourage annual servicing any more. What’s really sad about this is that some appliances (e.g. tumble dryers) are catching fire. A regular service by a skilled repairman may well have prevented some of these fires.
Servicing can’t stop many breakdowns
Some engineers may be reluctant to service a washing machine with no actual problems or symptoms. I know from experience, many faults cannot be detected, prevented or anticipated during a service. Once serviced, any faults within the next several months tend to get blamed on the engineer not doing the job properly.
Of course some breakdowns can be prevented. Some problems could be sorted before they worsen and became more expensive. But the overall lifetime of regular servicing costs would most likely outweigh these "potential" savings. If you look at it from a safety point of view though, then paying for a service is less about economy and more about safety. So there is definitely an argument for occasional servicing.
Don’t Ignore Faults
The most important thing to bear in mind is that symptoms of faults are ignored at your own risk. You must make sure you have read and understood all the instructions in the manual. Comply with do’s and don’ts, and look after it.
If you don’t have your appliance serviced you need to be extra careful about ignoring any symptoms. Leaks, noises, strange behaviour can all be signs of something that needs immediate attention.
I have seen many major faults that were caused by ignoring minor faults. Things like small leaks that can end up shorting out the electrics and damaging the main program timer. Or noises that eventually cause the drum or motor to seize up. Coins rattling about inside that eventually damage the main tub. If you don't want to have your washing machine serviced regularly – which is fair enough nowadays – at least make sure you don't ignore any symptoms that you become aware of.
Give your washing machine a regular service wash
I started recommending this in the early 1980s. Washing machine manufacturers all now recommend that you regularly put your washing machine on a service wash. This can prevent several problems caused by a build up of gunge and slime inside the washing machine. For further details read – Causes of grease, slime and black mould inside washing machine