Not only is it invalid, but we shouldn't even be involved in ME politics in the first place. So what if Trump cost a few Kurdish lives? The Kurds shouldn't be putting themselves at risk in the first place.
Do the Kurds want a country? Cool. Earn it, like we Americans did, with blood. If the Kurds do not have the will or enough blood to win that war, then they should have calculated that at the beginning and not go to war in the first place. Instead of a Kurdistan, be Kurdish-Turks, or Kurdish-Iranians or Kurdish-Iraqis, etc.
America's only interest in the ME is oil. Polite politics aside, we don't actually give a flying f* about your magic sky wizard of choice. America does. Not. Care. If your babies die. We care about oil. We will support any leader who also supports our policies regarding Oil. We will let stand any tyrant who supports our oil policies, we will oppose any innocent sovereign who disagrees with our policies on oil.
Oil is the modern currency of Earth and if you do not do what we want, we will kill you, because we play to win.
So, where do the Kurds stand with respect to oil?
Its not invalid. You have failed entirely to defeat the ratio of losses argument (Kurdish/US) or to even make that case.
The Kurds in and of themselves only really matter in humanitarian terms. Humanitarianism rarely counts for much in geopolitics. So I will value it as it is valued in the real world of geopolitics, pretty close to zero. Their desire for a country I would also value at zero with the exception of the degree to which it would support US National Security Interests for the Kurds to have a country. That is debatable. Not a slam dunk by any measure. That said that Syria is a country AT ALL is more the issue.
Syria as it is today was created via the UK's exit from the ME and its pin the tail on the donkey mapmaking effort in ME on their way out at least as a major military factor there. All Syria has is borders that Assad does not defend, borders that he has never defended. It has no visible means of sustenance. Its oil reserves are so tiny that their production to reserves ratio is not even reported. It has little arable land and had little arable land when its borders were created. It has even less now as it is the first of the world's countries that has suffered from climate change induced drought and famine. A good day for a Syrian ls surviving or alternately leaving. That is it!
The UK created other borders in their pin the tail on the donkey mapmaking effort but at least they left other countries with a visible means of sustenance. It left Syria with nothing. Assad has everything that matters in Syria. Everybody else is just trying to survive the next 24 hours. For the record the two real countries of the region based on tradition and history are Turkey and Iran. Iran is old Persia which is why the west really did not want to rape those people as we did. Iran as it turns out is the country that looks like and acts most like a country. It has tradition. It has history. It has pride and it has substantial visible means of sustenance. They have long memories as well.
In real terms the fact of the Kurdish alliance with the United States, an alliance that has ended in defeat not at the hands of their enemy but at the hands of their ally the United States and the geopolitical ramifications of taking such a direction and adopting such a position by the United States IS the issue.
In your third paragraph you almost got it. But not quite. Syria is strategically located such that it gives Putin, now the controlling influence in Syria since we are cutting and running, a ready launching pad to directly engage with countries that do have major oil reserves. Alternately, Iran, long Putin's ally now has what it has cherished for decades, a land bridge to the Mediterranean. A land bridge to the Mediterranean for Iran means that Israel, our ally is under a much more immediate threat from Iran than ever. At the very least, Israel and Saudi will have to play nice with Putin in order not to come under added pressure from Iran and Russia.
In geopolitical terms the United States lost big time. Putin won, big time. Assad gets to keep his personal wealth. So, he is happy. Assad is not more than a figurehead now. He does not even make puppet status. But he really does not care. Turkey wins big time though is far from the biggest winner in this. Biggest geopolitical winner by far is Putin. Second to him is Iran. Biggest geopolitical loser by far is the United States. Second biggest loser is Israel. Third biggest loser is Saudi although the Saudi's always figure to go to their standby strategy. Under threat of any sort they will lift their robes, bend over and let themselves get porked in some deal that allows them to survive and generate profits.
To understand any of this you will first have to learn how to read a map. That would at least be a start.