There is actually a good chance that the new coalition will survive, at least for a while, because it is based on the ancient principle that "the enemy of my enemy is my friend". And the enemy the two parties have in common is the European Union.
Until recently the M5S was promising to hold a referendum on Italy's membership in the euro, while the League was advocating outright withdrawal from the EU.
They have backed away from those extreme policies for the moment, but what they are promising to do will nevertheless bring them into direct and severe confrontation with the European Union.
The coalition's "contract for change", a joint programme agreed earlier this month, is a patchwork quilt of both parties' favourite policies. It includes the M5S pledge of a minimum basic income of €780 ($917) a month for the poorest Italians, and the League's demand for a flat tax of 15 per cent on the incomes of middle-class Italians, and only 20 per cent even for the rich.
This will doubtless please a great many Italian voters (the whole point), but it involves an extra $132 billion per year of deficit spending, and this blatantly violates the EU budget rules designed to keep the euro currency stable.
The Italian government's foreign debt is already so big that only the implicit guarantee of eurozone membership keeps its borrowing costs down.
A few more years of Italian over-spending, however, and the stability of the euro itself will come into question, so the EU will fight very hard to block the coalition's spending plans.
A confrontation is also likely to erupt over illegal immigration, with the new coalition government pushing for a change in the Dublin regulation that requires refugees to seek asylum in the first EU country they reach.
For the great majority of the refugees who make it across the Mediterranean each year, that first country is Italy, and most Italians want the burden shared more fairly among all the EU countries.
That would seem to be enough dry kindling to get the fire going, and yet an open fight between the Five Star-League coalition and the EU will probably be postponed for a while. It will get kicked down the road because the EU needs all the unity it can muster to resist the US assault on global trade.
The problem is not just the steep US tariffs on a variety of EU products that are due to kick in soon. The bigger issue is rapidly becoming how to protect European banks and companies trading with Iran from being forced to pull out of Iran by Trump's promised "secondary sanctions".
That's a sovereignty question, and the other big EU countries will bend over backward to keep Italy in line until this issue is settled.
In the longer run, however, a major confrontation between Italy and the rest of the EU is coming if the coalition government lasts.
For the EU to lose first the United Kingdom and then Italy would certainly look like carelessness, but it should not be seen as an inevitable event.
The narrow Brexit victory in the UK (52-48 per cent) was driven by a generation of English nationalists (Little Englanders) who are rapidly ageing out, while the great majority of the under-35s voted "remain".
The great majority of Italians want to stay in the EU, but their general discontent led many to vote for parties that are (among other things) anti-EU.
Some new EU members that spent almost half a century under Communist rule and very little time as democracies, like Poland and Hungary, are back under authoritarian rule, and the disease seems to be spreading.
It could turn into a perfect storm that unravels the European Union, but cheer up - at least Europe would recover some of its fine old traditions, like picturesque dictatorships and sporadic wars.
■Gwynne Dyer's new book, "Growing Pains: The Future of Democracy (and Work)", was published last month by Scribe in Australia, New Zealand, the US, Canada, and the UK.
