The question is not is the 1-3 trial task an appropriate way to find a new employee. The question is what barriers are there to most corporations doing this via paying for a 1-3 hour task.
The first is money. The company knows it costs money to find new employees. They know that they have to pay the HR person, they have to pay the hiring manager, and everybody involved with he interviews. Now you are asking for the ability to cut checks for $X to Y people to determine who should get the job. You will have to decide is this done to take everybody who passed the interview, or is it used to determine who will get an interview.
You will have to also spend time designing the task, and evaluating the task results. Which has to be paid for.
You will need to address internal applicants. If all finalist are being evaluated via the paid task, you will have to pay current employees also. Or only do this for positions not open to current employees. Which brings up other EEO issues.
You have to address how the pay will be processed. The applicants are now contractors. You will need social security numbers for everybody who gets paid. There will be tax issues - for both the company and the applicants.
Are you going to pay everybody. If I was unemployed and I could find enough people to pay me 3 hours to write a hello world program I might survive. Which brings us to unemployment benefits. To keep them I have to apply, but will the payment end the benefits because now I have worked for money.
Many of these are US centric issues, but similar issues might apply to other countries.