@raphjd
Lots to unpack there: thoughts meander much? 
In the early part of the pandemic, counting anyone who tested positive for the virus and subsequently died a victim of the disease was probably just a way to get around the fact that we knew SO LITTLE about it, and had little way of otherwise "filtering" results to get better data. Over time, all of that reporting will undoubtedly be revised for accuracy.
Forget the political leadership for a moment - the people who do the counting - who generate the reports - are usually career public health experts. In most cases, their only agenda is saving lives. (Fuckin weasly bastards!)
Now, what politicians do with that data is another thing... and in that, there is always politics. While I don't agree with any kind of playing with the numbers, I must say: I strongly prefer a politician fudging the numbers in an effort to save lives, over one fudging the numbers and sacrificing lives in the name of political expediency. Again: neither is good, but saving lives is still better than ignoring them.
I've already said - multiply now - that going back and re-examining our entire response - GLOBALLY - to the COVID-19 pandemic is definitely a wise thing to do... although, right now, I would personally rather that they keep focusing on getting through the pandemic... we can investigate early missteps once the threat has been reduced! Still, the only way we learn from our mistakes, is to discover them to begin with!
Finally: in the early days of COVID-19, we thought it was spread by contact - thus the suggestions you do things like wiping down your groceries before taking them into your house. Putting a sick patient you cannot help into a nursing home seemed, at the time, a humane way to let them die in peace, and in the presence of their families - while also freeing up badly needed space in the hospitals. The other patients in the nursing homes weren't exactly "visiting" the COVID-19 patients, and since there would be no cross-contact, it was thought to be a safe, humane way to treat the un-treatable.
It is important to put these things into the proper context: we had few treatments at the time that were effective once your disease got to a certain point... to put a fine point on it, yes: they were sent to the nursing homes to die!
And, as I've pointed out multiply already, we didn't know it was spread by aerosol. Thus, we didn't know we were exposing other nursing home patients to the disease... we thought the infection-control in the nursing homes would be adequate. (They were not)
It is also important to note that this practice wasn't wide-spread: it happened only in the hottest of the hot-spots... the biggest cities with the worst outbreaks. Hospital beds were desperately needed to treat the victims who were treatable and had some reasonable hope of survival.
It is not fair to judge their decisions or actions then based on what we know now! First, with the advanced therapeutics, immune-therapies, and other knowledge of how to treat COVID-19 (like putting patients on their stomachs!), there aren't many (any?) "un-treatable" patients any longer... while there is still a shortage of hospital beds, these patients have a decent chance to survive COVID-19 right up until the end, so there is no ethical rationale to send them elsewhere to die. Secondly, knowing now (what we didn't know then) - that COVID-19 is an aerosol disease - we would never put a dying patient anywhere that there wasn't a full quarantine in place.
While we (as a population) need to learn, and take heed, from the mistakes made in the early days of COVID-19 (and the US and UK are far from the only countries who struggled with their responses), care should be taken not to recriminate against people who were doing the best they could with little to no knowledge of what they were facing.
Simply put: we need to learn, but we do not need to blame.
