There is clearly a significant misunderstanding of the tests. There are 2: the lateral flow test and the PCR test. They are not used in the same way and they are not directly comparable.
The lateral flow is the one they use for surveillance testing of NHS staff, social care workers, in schools etc. It’s benefits are that it is relatively cheap and the results are quickly available. The downsides are that it has a high false negative rate, when compared to the PCR - some studies suggesting a false negative rate of 42-48%. We also know that self-administered tests (I.e. done by untrained people) are far more likely to give a false negative as people frequently do not carry them out correctly, but because it is simply not possible to have all the required lateral flow testing done by trained personnel, we have had to go with the less accurate self-administration set up. In addition, there is growing evidence that a single lateral flow test is not useful in terms of absolute positive or negative, but if done frequently (I.e. 2 or 3 times per week) that us the real benefit in terms of reducing spread. A lateral flow test can also be positive for some time after infection has resolved (in some cases it can many weeks). Taken together this is the reason why it lateral flow tests are used as a surveillance tool and not a diagnostic one. If you have a positive lateral flow, a PCR is used to confirm infection.
The PCR test is far more accurate (though still not 100%, but the best we have) but takes longer for the result. You could not use this for surveillance because it takes too long for the result to become available. There is faster version available but supplies are limited and much more expensive.
PCR tests are the diagnostic test for those who have symptoms or asymptomatic positive lateral flow. They are also used for ensuring negative status prior to planned hospital admission and to confirm whether emergency admissions are positive or not.
Given this it is not surprising that some countries want the most accurate test before allowing travellers in. It is also not surprising that this country might want testing before and in your return. Last years travelling was a significant contributory in last years autumn rise of cases. Non-essential holidays cannot be allowed to cause problems again.
Of course you should pay for your own tests for going on holiday. And you are paying not just for the costs of the test itself- you are also paying for use of the equipment, staff costs, and administrative costs etc. And yes, because it is a private company they will need to make a profit. If you don’t want to contribute to that profit, don’t pay for a test. Because NHS care is free at point of care, many people don’t really understand the true cost of what seem quite simple things.
NHS time and resources should not be used for those going on holiday. The time that is needed to process the test should not be wasted on doing tests for holiday makers. And why on earth should the costs of your holiday be subsidised by the NHS? If you want to go abroad (not essential) then you must factor this cost into your holiday. If it means you have to stay in this country this year, then that’s what you do.