If you want to reduce the amount you're withholding (so you pay less during the year, and receive less of a refund), you have to claim allowances. And the way those connect to the amount actually withheld isn't entirely straightforward (it's the tables starting on Page 48 at [1]).
And then it gets way more complicated if you have multiple sources of income, because the withholding calculations don't work in that case (underestimates your withholding, and you end up owing the IRS money at the end of the year).
I haven't seen the new form and can't say whether or not it's actually any better, but it can't be much worse; the current W-4 is one of those forms that looks simple ("just" two numbers to punch in) but turns out to be a fair bit more complicated.
Under penalties of perjury, I declare that I have examined this certificate and, to the best of my knowledge and belief, it is true, correct, and complete.
Where you must have at least an allowance of 1, for yourself. And why would you want fewer allowances? That results in more withholding, which is an interest free loan to the government.
You can claim a withholding exemption only if last year's tax liability was zero, and if you expect this year's tax liability will be zero.
Because you have investment income that is otherwise untaxed. I know someone who put 0 and still owed money at the end of the year, but didn't have to make quarterly payments. She had enough investment income to owe, but not enough to hit penalty levels of owing.
Nothing on the form states that the number of allowances you claim needs to match the worksheet’s results.
The IRS online calculator will explicitly give you different allowances to claim than the worksheet does.
The penalty of perjury would apply if you used a fake SSN or address.
If you have other income that's not easy to setup withholding on (such as stock related income, a home sale, or rental income), it can be useful to have more withholding from employment income. A benefit is that you are allowed to pretend withholding is evenly distributed over the year, even if it's not, or if it's more beneficial, you can use the actual timeline for withholding, although that takes a lot more effort.
Lines 5 and 6 are choices the taxpayer makes based on their expected level of withholding. The worksheet is not submitted, and not completed under penalty of perjury.
You can absolutely over-withhold and just put zero. The IRS has zero issue with that whatsoever.
The only way for me to avoid making payments is to specifically ask for an additional amount to be withheld in addition to claiming an allowance of 0.
[1] - https://www.irs.gov/pub/irs-dft/fw4--dft.pdf
EDIT: Apparently not. Would have been nice if TFA could have shown up the draft form?