The First Minister must be wondering what’s in the water at Westminster. Two of the fighting 56 SNP MPs, Angus MacNeil and the deputy parliamentary leader Stewart Hosie, are embroiled in a “love triangle”. Both men have parted company with their wives following affairs with the same woman, former actress Serena Cowdy. This follows two female MPs, Natalie McGarry and Michelle Thomson, being suspended following allegations of financial irregularity.

Now, sexual impropriety is practically a way of life in Westminster. Politicians living away from their husbands or wives often seek consolation in discreet affairs – though usually with different partners. This in no repeat of the “back to basics” omni-scandal that afflicted John Major's Tory government in the 1990s, as has been suggested. That was all about a hypocritical administration that played on “family values” being caught with its pants down.

With a metaphorical shake of the head, Ms Sturgeon got on with the business of reshuffling her cabinet yesterday hoping to draw a line under the affair. She has moved the powerhouse of her administration, former finance secretary John Swinney, to education, perhaps to take on local authorities and the teaching unions in her drive to improve standards. Fergus Ewing is moved from energy to allow an opening to the Greens on fracking, and there are hopes left winger Roseanna Cunningham will beef up land reform.

However, the SNP's critics on social media have wasted no time suggesting the SNP administration is in a state of moral decadence equivalent to the last days of Rome. In the wake of the loss of the SNP's overall majority in the Scottish Parliament, opposition leaders may hope they face a much weaker Nicola Sturgeon, beset by scandal, and forced to plead for votes to get her legislation through. They may have another thing coming.

The loss of her parliamentary majority could actually be a liberation for the First Minister, and not just because a referendum on independence is off the agenda. In a proportional parliament an absolute majority can be a liability. There is no revising chamber in Holyrood to weed out daft legislation and the committee system has tended to act as a rubber stamp. A leader, who has to rule on behalf of all of the electorate, becomes a prisoner of their own party.

Most of the mistakes made by the last SNP administration arose from it getting its own way. The most obvious was the Offensive Behaviour at Football etc Act, which is now universally derided as one of the worst pieces of legislation to emerge from Holyrood – “mince” as one Sheriff described it. The Act arose because of Alex Salmond's determination to “do something” about sectarianism. It was rushed through by a cabinet of yes-men and women and endorsed by SNP MSPs whose reluctance to criticise or question their leadership is legendary.

Looking back it's surprising there weren't more bad bills. Former Justice Secretary Kenny MacAskill's attempt to undermine the cardinal principle of Scots law by abolishing corroboration was narrowly avoided. The Named Person legislation got through, perhaps because it was buried in a compendious bill with more than a hundred clauses, and because Ms Sturgeon was persuaded that the “state guardians” would have a purely advisory role – as if serial child abusers are in the habit of seeking advice from teachers and health visitors.

First Ministers can't be everywhere at once. Ms Sturgeon needs Holyrood to keep her own administration on the straight and narrow. And in other respects, being a minority leader can be a positive. The opposition parties could, if they wanted, have prevented Ms Sturgeon becoming First Minister, had they worked together as they did in Wales, denying Labour's Carwyn Jones immediate preferment and undermining his authority as national leader. The reason they didn’t do this in Scotland is because they know they lack a mandate. Nothing better illustrates the authority of a true national leader than the fact the opposition daren't topple her.

In their speeches on Tuesday, the defeated party leaders made inflated claims of their influence. In terms they told Ms Sturgeon: “Ha – you're our prisoner now." But that is far from being the case. The former First Minister, Alex Salmond, wasn't a prisoner of the opposition parties when he only had 47 MSPs against Ms Sturgeon’s 63.

When the Green's withdrew support from Mr Salmond's 2009 budget at the last minute, many commentators, myself included, thought it might be the end for the minority SNP government. Mr Salmond held his ground, challenged the opposition parties to force an election, and waited. Within days, Labour was knocking on his door desperate to seek terms. Mr Salmond’s authority wasn't seriously challenged again.

Even when the government is defeated it can be a positive. It is likely Ms Sturgeon's first defeat will be on the OFBA – that is the only issue on which all the opposition parties are likely all to unite. She should accept that defeat gracefully, honouring the will of parliament and heaving a sigh of relief that she is off an uncomfortable legal hook. And if there is an uptick in sectarianism, well, she can’t be blamed.

The leaders of Labour, the Liberal Democrats and the Greens have all warned her not to seek to rely on Tory votes to get her way in parliament, or else they will accuse her of being a Tartan Tory. But this threat has been overblown also. Take abolition of the council tax, over which the non-Tory opposition parties hope to inflict another early defeat. Let's leave aside the fact it was the opposition parties who blocked the SNP's attempt after 2007 to introduce a local income tax.

If and when there is a vote on council tax reform, it will not be Tory votes that decide the matter but Tory abstentions. The First Minister cannot be held responsible for how opposition parties don't vote. Assuming Ruth Davidson sits on her hands on council tax reform, the record will simply show Kezia Dugdale, Patrick Harvie and Willie Rennie failed to muster sufficient support in parliament to force Ms Sturgeon to change her mind. Knowing that, they may decide not to force a vote in the first place.

On fracking, Ms Sturgeon might even welcome a move from the opposition parties. She would be able to argue she has to impose an outright ban, not on the science, but on force majeur in parliament. Even on independence, not having a majority can be a benefit. I don't expect there will be a huge demand among Scots voters for a repeat referendum after a Brexit vote, but if it happens, it will not be the SNP alone calling for the referendum. It will be parliament itself, in the shape of the SNP and the Scottish Greens. Downing Street will not be able to accuse Ms Sturgeon of having a personal obsession with reopening this issue if it is the will of parliament.

So, there's nothing the SNP leader can do about the sex lives of her elected members. But the more you think about it, losing her parliamentary majority could be the best thing that ever happened to Ms Sturgeon.