"It helps me sleep"
Plenty of people who'd give up the ten to seven glass without much fuss would fight for the one at ten. You have it, you get drowsy, you go up and you're gone in minutes. On nights without it you lie there. The conclusion seems to draw itself.
Sleep researchers have looked at this closely. In 2013 a team at the London Sleep Centre reviewed every study they could find of alcohol's effect on the sleep of healthy volunteers. At all doses alcohol shortened the time it took to fall asleep, and it made the first half of the night deeper and more solid. At all doses it also increased disruption in the second half. The first period of dreaming sleep, which is called REM sleep, came later than normal, and at moderate and high doses there was less REM sleep over the whole night.
The NHS says the same thing in plainer words. Alcohol can help some people fall asleep quickly, but it disrupts sleep patterns and stops you sleeping deeply, and cutting down should help you feel more rested when you wake.
This explains why the belief survives. You're awake for the part where alcohol helps. You notice dropping off. The cost comes hours later when you're in no state to notice causes. You surface at four with a dry mouth and a busy mind, or you sleep through and wake feeling you haven't, and you put it down to stress, or age, or the neighbour's security light. Hardly anyone lying awake at four thinks back to a glass of red at ten.
The cost then carries into the next day. A short, broken night makes for a thinner skin at work and a heavier tiredness by evening. That's the state you bring home at ten to seven, and it makes the glass feel more necessary than it did yesterday. Chapter 7 follows that thread.
The objection is a fair one. Without the nightcap you may well lie awake, at least at first. Trouble sleeping is on the NHS list of withdrawal symptoms for people who are dependent. For regular drinkers well short of that, a few unsettled nights after stopping are commonly reported, though I haven't found a study that puts a number on it. I'd expect it for a plain reason. If you've used a sedative to get to sleep every night for years, you're out of practice at doing it unaided.
I can't promise when that settles or that it will be quick. The argument rests on what the research above shows about the second half of the night. If your sleep is still poor after several weeks without alcohol, take that to your GP, because something else is going on and it can usually be helped.