The Conservatives are in trouble: send for Ruth Davidson? That’s the cry coming up from most of the centre-right and centrist commentariat, at any rate. Our own Chris Deerin is the latest to suggest that Davidson will swap Edinburgh for London in the not too distant future.

Davidson is clearly an upgrade on what the Tory party currently has up front and you can see how, as far as the centre-right goes, she is a lot better than anything else they might be able to offer as a candidate in the next Conservative leadership race. But there’s a problem: she already has a job and a seat in the Scottish parliament in Edinburgh – and I am yet to hear an even semi-plausible way she can exchange that for a seat in the Westminster parliament in London before the next election without doing fatal damage either to her brand or the Scottish Conservatives’ brand, or both. And without a seat in the Commons, you cannot run for the Tory leadership.

Davidson has ruled out any move until after the 2021 Scottish parliamentary elections and unlike Boris Johnson, who was able to go back on his word and re-enter parliament in the final year of his mayoral term, the strengths of her brand – at least as far as her fans go – cannot really survive going back on that.

So how can she switch Edinburgh for London after the 2021 elections? Let’s go through all of the possible ways that could play out. Start with the best case scenario for the Scottish Conservatives, which is that they win the Scottish parliamentary elections and are able to form a government afterwards. (I don’t think this is at all likely, but it is at least theoretically possible, so bear with me.) Her credentials as a Conservative who can win in places that other Conservatives cannot would be sky-high but, at that point, she could hardly declare that she was turning down the chance to actually run Scotland in order to be defeated by Sajid Javid in the run-off. So, that’s out.

Let’s say that she “wins” the Scottish parliamentary elections, in that she finishes first, but there are no viable coalition partners for her. (Again, I don’t think this is particularly likely.) Her brand as a winner is strengthened, but what is the justification that allows her to walk out of Scottish politics? Declaring that one of her parliamentary flock is better-placed than her to finish the job and do well enough to govern next time? Hard to do that and claim that you are the best candidate for the job in Westminster. Declare that it is impossible for the Scottish Conservatives to do better and that their upper limit is a moral victory in which the parties of left and centre lock them out of power? What’s the point of the Scottish Tories then?

Now let’s say that the Scottish Conservatives only do as well as they did in 2016 – still comfortably the largest opposition party, but the SNP are still in office. This is considerably more plausible than the first two options and is what would happen if current polling plays out at the next Scottish election. And again, the same problem: it is easy to see what Davidson’s exit from the Scottish parliament – Rexit? – looks like, but hard to conceive of a way that she can do it that doesn’t either damage her own brand as an electoral asset, by declaring that another Scottish Tory can do better than her, or damage the Scottish Conservatives by effectively declaring that second place is the best they can ever do.

Then you have the nightmare scenario for Davidson: the Scottish Conservatives doing worse at the next Scottish election than they did at the last. She wouldn’t struggle to finesse the terms of her exit from the party leadership then, but her brand as a sure-fire winner would have taken major damage.

You can just about draw up some fantasy scenario in which the Scottish Conservatives do better than in 2016 but Davidson loses her own seat of Edinburgh Central, which allows her and her party to part ways without suffering undue damage. You can see how a narrative around tactical voting might work there but it is such an implausible combination of events (you can see how the Scottish Tories do better than they did in 2016 in 2021, you can see how Davidson loses Edinburgh Central... it’s very hard to see how both could happen on the same night) that it is almost not worth mentioning.

But let’s say that somehow, there is a justification for the transition that doesn’t cause the Scottish Conservatives or Ruth Davidson some political damage. How does she then go from the parliament in Edinburgh to the parliament in London in time to become Tory leader before the next election?

One thing that we shouldn’t have forgotten when the snap election happened is that voters don’t like being made to vote more often than they feel they ought to, and particularly dislike it when they feel they are being made to vote because of the machinations of politicians. That is part of why Labour lost the 1965 Leyton by-election – manufactured to give Patrick Gordon Walker a seat – part of why Ted Heath lost his majority in the 1974 election and part of why Theresa May lost her majority in 2017.

And Leyton was an ultra-safe Labour seat in a much more tribal era. It is by no means certain than even the safest of seats is a sure-fire way in at a by-election, particularly not for a Conservative Party that would, at that point, have been in power for 11 years and implementing painful spending cuts for at least the majority of that time. That said– to return again to the matter of Davidson’s brand – I can’t see how that by-election could be anywhere other than one of the 13 seats that the Conservative Party holds in Scotland. Some of those seats now have very large majorities indeed, but they also have incumbents who may not wish to vacate them. Crucially we have seen, in two successive elections in Scotland, how very large majorities can crumble very quickly. Even more importantly, part the Scottish Conservatives’s success lay in cannibalising the votes of the parties of the Union. That is obviously a viable strategy at a general election, whether that be to Holyrood or Westminster. At a by-election, when the stakes are lower and the opportunity is there to take a free hit at the government, it is less clear that it is a viable strategy.

None of which is to say that it is impossible for Ruth Davidson to navigate the Scottish elections and a by-election to become an MP in time to participate in the next Tory leadership election. But it is to say that any analysis based on the idea that she will be the Conservative standard-bearer at the next election has to reckon with the considerable and dangerous obstacles she will have to overcome to get there.