It started out as one thing, but the primary reason these days is that it keeps a finger in Russia’s eye. What the actual end state desired is, I have no idea. In 2021, as a brigade operations officer over there, I asked the commanding general what the strategic goals were for Syria. I’ll keep the details to myself, but he more or less said that he would like to know that, too. And that was before Russia invaded Ukraine and introduced even greater complexity to the geopolitical situation.
That was the problem from the beginning - no end state would be good for US. Always made it difficult. The Russian had a long relationship with Assad and a naval base - the Iranians the Shiite crescent. But we had no positive outcome to pursue.
Well that's the problem with our foreign policy in general. What is our goal? Global democracies? Stick a finger in Russia's eye, prevent China from becoming a superpower? You can't ask our military to do all of those well, it's just too expensive. That's kind of our problem right now is we don't have a good strategy, it's all "Well here is a list of problems" and throw money and people in harms way. Very poor leadership, and it's been that way for a long time.