Was that really the very best we could do? That question hangs unspoken in the air at the Scottish Covid inquiry like a bitter rebuke.

The inquiry is currently taking a series of impact statements from families affected by care home rules and on Tuesday, we heard from Natasha Hamilton.

Before the pandemic Natasha often visited her mum Anne Duke, who had dementia, in a care home. She would hold Anne’s hand and sing songs with her. She told the inquiry how much she cherished those moments.

But everything changed when the pandemic struck. Natasha wept as she described how in November 2021, she missed her mother’s death by seconds as she had first to get the results of a Covid PCR test and then “wait her turn” to go into Anne’s room because visits by relatives were being staggered. Her father and sister were present when Anne died; Natasha was not.

Read more Rebecca McQuillan: Boris Johnson thought old people were expendable – but it turned out he was 

Natasha’s father Campbell Duke regarded his wife as being “imprisoned” in the home for months on end and called the policy “despicable, heartless and relentless”.

It’s the latest in a harrowing series of testimonies about care during the pandemic.

Down in London at the UK Covid Inquiry, we heard more about what was happening in 2020 in the engine room of the British state. Yesterday it was the turn of Lord Mark Sedwill, who was the UK’s most senior civil servant in those difficult days.

The archetypal mandarin – polite, measured and deft at tiptoeing through verbal minefields – the former cabinet secretary apologised for remarks made in private that chickenpox-style parties could be held for Covid early in the pandemic when it seemed “inevitable” that the virus would spread. He said he knew Covid was a more serious illness than chickenpox.

We heard yet again about a lack of faith in health secretary Matt Hancock, whom Sedwill admits he told Johnson to replace (Johnson didn’t for another 12 months). He also confirmed he had concerns about decision-making, having to remind Boris Johnson to involve the cabinet in decision-making (instead of relying on a small coterie of advisers).

Again: is that the best that we the public had the right to expect?

That is what these inquiries are supposed to establish. Both are tasked with learning lessons, particularly in relation to pandemics.

But they are proving to be much more than that. They are developing into a wholesale management review of government, with implications that go well beyond the handling of the pandemic.

The Scottish inquiry is exposing pain caused to families as a result of rules developed by officials. Those rules were made in good faith in the face of a virus for which there was no vaccination, but even so, were they inhumane? Were officials and ministers connected enough to the experience of people at the sharp end?

Are they now?

The UK inquiry meanwhile continues to show up problem after problem in the way decisions were made then and even shedding light on governments’ claim to be transparent now. Suggestions that Nicola Sturgeon may not have kept all her pandemic-era WhatsApp messages and that ministers and officials had leeway to edit what they did save are making ministers squirm.

Read more Rebecca McQuillan: How can ministers help the creaking NHS? Be brave on public health

But yesterday’s focus was once again on Boris Johnson and his team in Downing Street, where issues have surged to the fore about diversity and respectful working relationships (or a lack thereof), ministerial incompetence, optimism bias and the Prime Minister’s overconfidence that are salient in every context, not just the pandemic.

This pitiless behind-the-curtain view would flatter no-one, but the value of it can’t be in doubt. These are cultural issues. The question is whether governments across the UK are paying attention. If it were their operations right now, today, that were under public scrutiny in a neon-lit conference room, then how well would they come out of it?

One of the most striking lessons from the UK inquiry has been the apparent failure in Downing Street to ensure a mix of individuals from across society were involved in decision-making.

Diversity is one of those words that elicit small sighs and sceptical eye-rolls from those who see it as tokenism and corporate box-ticking.

But any woman who has had their point dismissed in a room full of men will understand how important it is.

Last week senior civil servant Helen MacNamara revealed a culture towards women that seemed to have survived unchanged from the 1990s. She herself was the subject of a foul-mouthed misogynist message from Dominic Cummings which went unchallenged by the PM.

MacNamara said the government was a “toxic environment” where female civil servants found they had “become invisible overnight”. Because of this, she said issues like domestic violence, the plight of those with caring responsibilities, pregnancy and PPE for women, were inadequately dealt with – issues that collectively defined millions of women’s experience during the pandemic.

She feared that the lack of provision for domestic abuse survivors in the first lockdown in 2020 actually contributed to women’s deaths.

Remember that this is not the hyperbolic insinuation of a campaigner: this is the considered view of a veteran official about government decision-making during Covid.

So yes, diversity matters.

All in all, an unflattering picture emerges from the testimony we’ve had so far of meetings populated by hubristic, cocky men who failed invite diverse points of view. People who didn’t look or sound like them may have paid the price.

Depressing? Yes, but these insights are valuable.

We deserved better, that much is clear. But they also lead to this question: what is the picture now?

How respectful are relationships between staff in Downing Street today? Does optimism bias still infect decision-making? Are women and minority groups any better heard at the heart of the UK government?

There’s a long way to run with these inquiries but already they are raising uncomfortable but crucial questions that every department of every government should be asking of themselves.