Well, that’s an easy one.

They would be able to sell more beer and stuff. Some churches would probably get upset. Maybe a few idiots would get squiffy and throw peanuts at the police.
And life would go on.

Overindulging in capitalism

Certainly, overindulgence - whether a race to get slack-jawed, dribblingly horizontal or years of statistically significant, cumulative use - can and does have drastic physical and mental effects. Equally, people are more than capable of risk-assessment and intelligent analysis of what ingesting substances will do to them.
There is a section in any community that is more prone to excess than others. You could have ale shops open for only half an hour a day and some people would still find their way to getting wasted. In countries with extremely high duty (even higher than Cayman) like Iceland or parts of Scandinavia there’s a huge tradition of home distilling for this very reason. Brings a whole new meaning to the phrase ‘blind drunk’.
And look at what happened with Prohibition. Hardly a roaring success, that, was it? Unless you were a rum runner, of course. God bless capitalism.

Two arguments in favour of keeping liquor stores open longer:

The economy is broken and store owners need to survive.
Everywhere else seems to do it.

And against:
People would be able to buy drink.
See point 1.

Tourists and tarpon beware

The truth is that there’s nobody with a gun at your head forcing you to get drunk; there’s no reason why, on walking past an open liquor store, the compulsion will suddenly be there to neck a bottle of mother’s ruin, get naked, jump in the water and carve swastikas into passing tarpon.

Indeed, I would be willing to bet (though obviously not for money, for that is also bad and wrong) that the vast majority of us walk past several open bars every day (which serve alcohol well into the night, by the way) without feeling the need to detour for an eight-hour binge of Absinth and fire cocktails before joining a black metal cover band and shooting bolts of devil-driven wild guitar feedback at huddling packs of shuddering-jowled lobster-tanned tourists looking down the road the wrong way.
Here is the news: having a drink is not the same as being a drunk.

Addicts are not criminals

Drinking is not a social problem, but addiction is. Changing access hours, delivery restrictions, can only ever be plastering over the cracks in a society that cares more for outward appearances than underlying issues. Because addiction’s not a crime. Overindulgence in itself isn’t a crime.

If a society wants to simultaneously tax, consume and vilify a legal substance - as it seems to do - then it ought to look at its
motivation. It’s a particularly human trait to be able to hold such stunning double - or triple - standards, but not a particularly useful or progressive one.

Opening up liquor stores a little later in the evening has very, very little to do with any of that.

Because it’s always five o clock, somewhere.

There’s nobody with a gun at your head forcing you to get drunk.