Such a thing is indeed possible - but only when your data is already complete and accurate. This poses two questions: is everything there? and is everything accurate? The latter is more difficult because often information is required that you may know is required. That is why accountants use questionnaires.
When you buy any service, you weigh up three factors: speed, cost and quality. A common trade-off is paying extra for a faster service, or less for a slower service. Of course, some vendors charge but don't deliver speed or quality, but let's focus on those who do want to please.
The Warehouse is a classic example of a business focussed on price. They don't appeal to everyone - but attract customers because of low prices. Quality is more difficult to evaluate. Buying a tool or appliance can be a case of more expensive lasts longer or offers more functions. But it can also mean you get less visible extras - such as service and warranties. Or it may be that the supplier's view of value differs from competitors. The same applies to services - but often less visibly.
When it comes to tax returns, quality can be very difficult to judge. Cost is often higher than expected when the fee is not fixed in advance - or when the quality of your bookkeeping is less than ideal. But the quality of the service is hard to discern for the layperson.
We opt-out of competing solely on price. If you simply want the cheapest tax returns done, do it yourself. The government is planning to make this "simpler", so why not? Alternatively, there are comparatively cheap services out there - but they can be difficult to evaluate. People offering tax services don't provide the number of clients they've lost - and the reasons why they lost them. Death, retirement and other forms of business cessation are a fact of life. But the others would be really interesting to know more about.
A classic was a client who came to us trying to recover over $50,000 he'd lost because his former advisor had not timed things correctly. Sadly this could not be altered. This shows two potential problems with a cheap tax job. The advisor may not be up to scratch - or you may leave things until the end of the year - which is sometimes too late.
The first thing I suggest about getting a quality advisor is to use a professional accountant (CPA or CA in public practice). This does not guarantee you will get on with them personally (we accountants are a funny breed). Nor does it guarantee they will get everything right. It does give you a better chance of having any wrongs rectified, either through their professional body or through their mandatory professional indemnity insurance.
Just because someone doesn't belong to either professional body doesn't mean they don't do a good job. However, the odds of getting a poor job from a professional (who is subject to continuing education and practice review) are relatively low. I can't say what the odds are of getting a good job from a non-professional. Suffice to say I have seen too many flawed jobs done by people who call themselves accountants, or by book-keepers who often don't recognise when they're in dangerous territory.