But I somehow don't really understand how come some users (especially still using old wiring and antenna), have to power on the masthead amplifier (booster) to get digital TV signals. I'm referring to the masthead amplifier used during the old analogue TV era (e.g. typically the orange box under rooftop UHF antenna, and a small white box near TV that connects to power).
They need to power it on to receive digital TV signals.
If they power it off, no signal. Or some users is, if power on the masthead amp, no signal, but once power off, it'll have signal but not high and unstable.

Is it because the antenna used is degraded cable or it's not RG-6? Or the antenna is too little "elements" or not powerful enough? Or simply because TV transmitter distance is too far away? Or what?

This is kinda contradicting, cuz some or many people may think that to receive digital TV signals today, using a masthead amplifier (booster) is as necessary as getting analogue TV reception like decades ago. Cuz some users find that without booster, they can't get adequate or no signal at all.

Changing/rewire to the new RG-6 cable will greatly improve the signal reception, so does it "guarantees" that digital TV viewers today are seriously no need to use masthead amplifier (booster) anymore and they can throw it away already? As long is:

Outdoor UHF antenna + RG6 cable (properly terminated) = You've tried your best to get digital TV signal.

My antenna is the cheap rabbit ears type. Not sure its UHF or not.