But many do because you have a tiny chance to win a lottery. Yes, they do it even for one coffee (0.70 euro...).
I do not understand why there is still no system to easily transfer that fiscal number. For example with a qrcode or RFID. You pay electronically with card, often only by just touching your card, phone or even watch, but then have to give a memorized 9 digit number which the deskperson has to type correctly.
You can. The VAT number is used to enter you in a lottery where you get a small chance to win some of the taxes you paid back, but that is optional. The goal of the system is to increase compliance with tax laws, by having consumers ask businesses for receipts and pressure them into paying VAT.