Not that I am for a moment suggesting that this is happening...but if you were a government who would quite like the numbers to not look too bad, wouldn't one way of achieving that be to mess up the supply of tests? Asking for a friend...
I dont think they are actually interested in making the numbers look better at this particular stage.
Thats something they might like to achieve in future, but at this stage of this wave such things have been utterly trumped by other priorities.
They have their eyes on a bigger prize - to have a peak and decline that isnt lockdown-induced. And in order to stand some chance of that happening, they left certain brakes in place. Some of those brakes involve testing and contact tracing/the app. As we have seen via the recent emphasis on the 'pingdemic' by the media, the self-isolation stuff is a very big deal in terms of the numbers of people that it affects and the disruption that it causes. But some of that disruption is to the viruses ability to find ever increasing numbers of victims. So the self-isolation stuff, during the peak period of a wave, becames a sort of mini lockdown by stealth. This disruption makes the government look bad, but clearly they felt that they couldnt make the wave planning numbers add up if they removed those brakes at this particular stage. So even though the disruption makes them look really bad, they didnt even want to fiddle with the app sensitivity at this stage despite all the pressure. And I take that as a further indication that they realise that the self-isolation brakes are still very much required at this stage to prevent hospitalisation numbers soaring beyond the limits. They would much, much rather this big disruption and mess for a number of weeks than having to u-turn on key irreversible relaxation pledges by bringing back other forms of brake.
And I think that any temptation to 'fake the peak' via test system limitations is removed by the fact that we'll be able to see the real peak via hospital data later anyway. Plus authorities have not tended to prematurely jump at possible peaks in the case data either, they have tended to use cautious language about peaks and not to describe them as such until a fair amount of time had gone by since the positive test data implied a peak. Scotland was a recent example - they didnt acknowledge the case peak much at all to start with, then used language like levelling off when the numbers had actually been falling for a while, and only in recent days started to talk about the declines. In other words authorities tend to wait until multiple different sorts of data confirm the peak, and arent keen to make fools of themselves by describing something as a peak if theres a fair chance it will later turn out to be an artefact of the testing system rather than a real peak.
Plus the government made a huge deal of how large the case numbers could become in this country, by chucking around figures like 100,000 per day. Now it is possible that they gave a very large number because they were hoping the real number would be lower than that so they could be all triumphant about it. But again they know that the hospitalisation figures and deaths are what really count, so the potential gains from fucking around with case numbers arent very high.
And it makes them look bad when the testing system turns out to be unable to cope. And there are measures such as percentage of tests returning positive which are used to judge such matters and to make educated guesses about reality vs what the daily positive numbers are. And there are infection surveys that use random household testing to demonstrate the scale and direction of travel.