So I caught up to the end of this show now. Late, I know, but my time for watching these shows is limited and my patience for LoT has been dropping for a while, so I just wound up prioritizing new episodes of other shows over catching up to this one.
Overall I would say season 2 did improve on season 1 in terms of characters. It maintained the humor for the most part. But the action is increasingly disappointing - Firestorm being sidelined for no reason is practically expected at this point, and most of the second half of this season the only characters who routinely used their powers were Nate and Amaya (the cheapest and least visually interesting powers). The time travel aspect is increasingly less fun, since it never makes any sense anyway and the stories they're telling are mostly just lame (Rory lecturing George Washington about America? Really?). And with the characters total lack of moral consistency or any concern for the consequences of their actions, it's difficult to even root for them at all anymore. Especially in regards to this finale, it's hard to even see how the Legends aren't actually just villains at this point. Doomworld may have been illegitimate and corrupt, but at least Thawne didn't jeopardize the entire universe to get his life back.
It basically comes down to the fact that the non-sensical nature of everything just keeps getting worse. Someone mentioned a few pages back how they were running out of patience with Supergirl's ongoing massive plot holes, but for my part this show is a thousand times worse at this point. I get the campy idea, but if you want me to just turn my brain off like that, then show me something truly off-kilter (like Adam West trying to get rid of a bomb). This show is still trying to present itself realistically even though its simultaneously not making the slightest effort to take itself seriously and it continues to ask me to emotionally invest in characters who are inevitably at the mercy of incomprehensible writing. It just isn't working for me at all.