Is it reasonable to qualify a component by testing only?
I am going to defend the practice. As long as your company is willing and able to do the necessary testing to qualify the components for use in your company's products there is nothing wrong with violating data sheet parameters for the component. This does require some knowledge and skill and experience because the test suite needs to be well designed and properly executed. It may be easier to find components that are rated for your intended use because intense component qualification programs do require the company to commit a lot of resources.

Obviously, it is important that the supplier have good process controls in place so that you will not encounter unexpected variations. This is definitely something that needs to be discussed with the supplier so they understand that you need to be notified of any design or process changes for the component. Many suppliers are accustomed to operating that way already so this is not necessarily a new burden for the supplier. There is the question of recourse in the event of failure. If you have problems with a batch of parts, the supplier may not take them back if they meet datasheet parameters. So dialog with the supplier ahead of time is necessary.

Ultimately, products made on assembly lines are generally very similar to each other. That is the whole point of the assembly line. It is reasonable to assume that products made tomorrow will behave the same way as products made yesterday on the same line. When clusters of defective products are found, they can usually be traced back to a change of some kind in process or testing or a supplier who made a change without telling the customer.

Once during product qualification for a consumer product I found that there was a bus timing violation. We were not meeting the setup time. My boss told me to talk to the supplier and find out what the real setup time was, as opposed to the one in the datasheet. What? WTF is he talking about? But he was right. The datasheet specification was an exact, parameter-by-parameter copy of a part they were competing against. The real setup time was much, much more permissive and they performed 100% internal testing to verify it and showed me test reports. They would not change the datasheet because the parameter match parity was too important. Sometimes component engineers might reject the part as a drop-in replacement if any parameter is different.

So, sometimes the motivation behind specifications in a datasheet is not what you think.

I am very skeptical, honestly, that a 10A switch could handle 20A. My comments are more on the concept of qualifying by test for things that are outside the datasheet specification. Not necessarily in direct excess, but just outside the scope. I got the impression from the OP's post that the question was about the general concept and not about the specific switch (which does sound dubious). But if someone asked me to approve using a 10A switch with a 20A load I would start by doing a heat rise test and then try to weld the contacts by interrupting an inductive load like a motor.

But also, it is a mistake to ignore history. If the switch has been in use for mass production for a long time and it is well known that it has not caused reliability problems, then for goodness sake don't change it now.