In the UK quite a few people don't pay any tax at all, and the vast majority don't pay enough tax to have to file any return.
What impact does a dependent have on your tax that needs to make it so complicated? I have relatively complicated taxes due to two jobs and some unusual deductions, but having a child doesn't really have any impact on my tax return in the UK.
As for the dollar values, if you make $30,000 and have 2 kids, you can usually get a $6,000 tax credit or more. The U.S.'s support for working low-income families is carried out through the tax system. Put another way, tax credits are one of the U.S.'s most important social safety nets.
No matter the situation, they accept your word for it. If an audit occurs you will have to prove things with documentation and be held liable for mistakes or fraud.
It's basically a five-minute task that you appear to believe should make tax filing take hours?
I did taxes once in NZ, you go to a website where they have all the data ready. Then you go next, next, finish, adding a deduction or dependent here and there. Takes 15-30 mins.