Politics is not about morality. Morality is just a fig leaf. It's fine for Kosovars to vote for independence and secede but not for Kurds. There is no consistency.
Here are my thoughts.
1. The US is in reality very in favour of an independent Kurdish state and has tried to facilitate that including in Syria. However they know it's something that the regional powers (and "powers" is a carefully chosen word because with a declining US these states, Iran, Turkey, Syria etc with their militaries have a lot of real physical power in this region and this issue) will never accept. So rather than lose face by endorsing an unachievable independence for Kurdistan they are poo-pooing the idea.
2. For the regional powers in the area i.e. Turkey, Iran, Syria, Iraq and even to a lesser extent Russia and China they will never accept Kurdish independence as it constitutes a threat to their very national security and continued existence, to their survival.
A Kurdish state (be it in Iraq or Syria) would embolden Kurds in Turkey and Iran. In the Iranian context if the Kurds were to secede then the Azeris and Baloch could be next. The Azeris have Azerbaijan and Turkey which are their ethnic kin next door. This could spell the dissolution of the Iranian state. The Turks feel the same way and that if Kurds in Turkey were to see an independent Kurdish state they may try and secede too and the consequent possible knock-on effect on other minorities.
3. The truth is unlike Iran, Turkey isn't really a multi-national state Yes there are different ethnicities and communities such as the Laz, Hemsin, Bosniaks, Circassians but for them these sub-identities are unimportant and akin to an American saying how he had a Swedish great grandfather, nothing beyond a pleasantry but nothing that would swerve his loyalty away from America. However the Turks are a traumatized nation forever living in the ghost of the "Treaty of Sevres" which could have meant Anatolia being carved up. Since then for decades the Turks especially their military have been ultra-paranoid about the possible break up of Turkey, despite the fact that the only true nation aside from "Turks" (Turkish-speaking Muslims) in Turkey are the Kurds.
Iran however is very much a multi-national state like the ex-Yugoslavia was. However the Turkish paranoia will mean they will never allow a Kurdish state to exist.
4. The Iraqis won't allow the Kurds to secede and will use military means. They would work with Turkey in sealing the Iraqi-Kurdish border with Turkey and thus thwarting the emergence of a Kurdish state.
5. The Syrians have been in a 7 year war and have reconquered most of their land including big cities such as Aleppo. They've destroyed the AKP/Erdogan dream of "neo-Ottomanism" and are on a wave and are planning to recapture Kurdish held areas. The Iranians, Iraqis and Turks all support them.
6. The Kurds timed their independence vote at a bad time, coinciding with the Catalan referendum.
The EU fears that if the Catalans secede from Spain this could trigger a wave of similar secessions in other parts of the EU.
There is a small region of southern France which is historically Catalan and for them to be next to an independent Catalan state though not a major concern would be something Paris would prefer not to exist. More signficiantly, there was a virtually dead language called Occitan which was widely used in southern France and is quite similar to Catalan. In the future if the southern French revive their interest in their almost forgotten Occitan tongue it could be the embryonic seeds of desires for autonomy stemming from a perceived sense of being a culturally and linguistically distinct region.
Italy also has secessionist issues.
The EU prefers member states to stay intact rather than splinter and fragment in to countless mini-states which is logistically more difficult for the EU.
a: All 25+ languages (27 members but 24 official languages as some countries e.g. Germany, Austria speak the same language. It becomes 25 when you add Catalan and could become more if other regions secede) would need to be translated with the additional burden of Catalan.
b: Another interest needs to be accommodated, you have 27 "egos" and "interests" to reconcile in the form of the member states and it becomes even more difficult to reconcile 28. Not to mention the possible feud between Spain and Catalonia that could emerge.
So considering all this it's not strange that there is no great interest or support for the anyway unattainable goal of Kurdish independence (unattainable since 4 states with 4 relatively big militaries, Turkey has the biggest army in Europe would stop it).
7. The Chinese are very conservative in their foreign policy and dealings and are very non-interventionalist including the belief in the integrity of sovereign states, not just because it would undermine themselves and their Tibetan and Uighur secessionists but also they are generally conservative and do not want the headache of new unknown entities to have to deal with.
8. The Russians are allies with Syria, Iran and Iraq and increasingly more so with Turkey. Also secessionism is not something they encourage as they are a multi-ethnic federation.
9. The Pakistanis are also a multi-ethnic federation and just as the Turks are scarred by the "Treaty of Sevres", the Pakistanis are scarred by their humiliation in 1971 and do not want the break up of their state.
Also Kurdish nationalists are very pro-Baloch and this would only strengthen Baloch separatists.