You have a chance of a job at a household name company (who can afford to be selective) , probably with cushy salary and benefits.
8-10 hours worth of work isn't a great deal, especially if they give you a few weeks. Even a person working a full time job should be able to squeeze that in by temporarily reducing hours spent watching TV.
It's not like facebook even get any benefit from you performing this work for them.
There are many such companies out there and the better ones will talk to you politely first, look at previous work you've done and then perhaps invite you over for a couple of interviews (including some code puzzles). I was once flown from Europe to Florida before any code puzzles, got to see the whole company, talk to founders (the company was a subsidiary of a household name in games) and technical directors before sitting down for some tests. It was a great experience and I felt very bad for turning down the job offer because they treated me so well ...
Google and Facebook I'd avoid from what I've heard (no firsthand experience though), they seem to hire talent just to keep it away from the competition.
Therefore they need some way to filter people quickly. Would it be better to do this purely on the basis of resume? Forcing people to invest time making sure they have the correct mixture of buzzwords or would you rather spend that time demonstrating that you can actually code?
This really depends on whether they chose particular people to contact directly or whether those applicants contacted the company.
Sure, the 1000s of applications these companies get every month must be filtered quickly, but if someone was selected for a "cold call" by the employer (presumably based on some research), then handing him menial tasks upfront is a terrible idea and unacceptable for the probably more skilled people typically contacted this way.