It's bonkers, of course, but there's a political head of steam behind it which could prove hard to resist. There's a general climate of wanting to slap restrictions on any place which sells a drink whenever the opportunity presents itself.
Here's what's afoot in the two neighbour cities. Under the 2005 Licensing Act licensing boards are legally required to draw up an overprovision policy, and that's a perfectly reasonable thing for them to do.
But both Glasgow and Edinburgh are currently gearing up to interpret this as a mandate effectively to kill off any new trade endeavour in some of their most popular dining and drinking areas.
It doesn't matter that the number of licences is down, overall, or that it can be proved that most people increasingly drink at home. Newspaper headlines keep telling us we're all drinking too much; and TV footage continually illustrates stories of drink abuse with footage of people falling about drunk in Glasgow weekend hotspots like Sauchiehall Street (which of course they do).
It's not the number of pubs which is to blame for disorder, but the concentration in key drinking strips of Friday-nighters already well primed with cut price booze from supermarkets.
I know this - I regularly watch prospective "revellers" in the supermarket queues buying the liquid pre-load ammunition while planning their night's on trade adventure.
Meanwhile residents see drunks wandering about at all hours, committing all sorts of atrocities in their gardens, and then lash out at everything running a bar - even in areas that don't have problems with drunks.
We're now at the point where the tide of hate directed at pubs has become so all-pervasive that logic and commonsense no longer seem to have any role to play.
If you sell drink, it seems, you're part of an industry dedicated towards getting Glasgow or Edinburgh blitzed. If only people would stop opening new bars then everybody would stay at home and behave themselves.
In Glasgow (where the city centre scene at weekends is, admittedly, not pretty) the mooted licence freeze would be applied to seven main areas. One of them is the trade-busy West End which also has far and away Scotland's highest concentration of quality bars and restaurants.
In Edinburgh the main focus has been the Cowgate area of the Old Town, an extremely lively strip continually blamed for filling the nearby Grassmarket (right underneath historic Edinburgh castle) with hordes of maudlin, vomiting drunks in the early hours of the morning.
Yet the last time they brought in a licence freeze in Edinburgh Old Town the high end Hotel Du Vin - not known for hordes of maudlin drunks - had to jump through all sorts of hoops to open an outlet there including, naturally, a bar.
In such a fierce environment why would anyone even consider opening another bar, when the problems of making a decent profit are so well known?
The answer can be found particularly in Glasgow's West End. True there are some areas which are raucous and a bit seedy at weekends, and I can see an argument for deciding there are enough large units to be going on with.
However rather different is a brand new cafe-bar, The Criterion, in a street where a few years ago there was next to nothing in the way of a trade presence.
This place, a little art deco design masterpiece, is now one of three outlets in a row, all different, all critically rated for food, ambience, quality of service, and individual flair - all distinctly above average yet not wildly overpriced or self-consciously "posh".
They've been converted, amid many planning travails, from defunct shops, and, ludicrously, they're all the sort of places - civilised places - a blanket freeze policy could have prevented ever from opening.
Operator Allan Mawn, who around two decades ago opened Glasgow's first Hispanic restaurant a mile along the road, should be receiving some sort of civic honour for his enterprise rather than the implicit threat that he (or some other operator trying the same sort of thing) could be blocked out by a moratorium on new venues.
Bring in a freeze and some operator like Allan could watch and wait for one of the sacrosanct existing licences to fall vacant, then join the stampede to acquire it - but chances are he could be beaten to the finish line by something corporate and dull.
Do we want Barcelona or Cumbernauld? - that is the question.
I'm not suggesting we need large numbers of new units opening all over the place, and that will never happen anyway because of the level of competition: if a pub or cafe-bar doesn't capture its audience it won't stand the pace.
But the new licensing set-up has plenty of checks and balances built in to prevent just any old bar from opening - so why get tough on the entire licensed trade and everyone in it?
A licence freeze won't solve anti-social weekend drinking in popular strips where it happens, but will prevent operators developing outlets which can radically transform the whole character of an area for the better.
Change the drinking "vibe" of a district, an important part of its social culture, and you achieve much more than you could possibly hope to gain by simply limiting the theoretic capacity of every kind of trade unit, all lumped together.
Take the trouble to visit individual outlets like Allan Mawn's, in fact, and decision makers might start to realise that we need to civilise, not sanitise.