I agree with many of the points that were brought up here already. While I enjoyed most of the sequels, I too feel that they could and should have been made darker. We get occasional glimmers of dark moments, but as Bruton said, it did feel like Universal was holding back. The sequels still had a lot of good character development to make up for it. But Littlefoot never went through the same struggle that he did in the original film, and I wish that he and the other members of the Gang had.
I don't think it would've been hard to make the films a bit grittier; the same basic plotlines could've still worked. And in fact, there's aspects of said plotlines that would lend themselves well to darker scenarios. Like in LBT 2 with the very concept of the egg-stealers and Chomper's parents, or in LBT 3 with the Great Valley facing a drought, or in LBT 5 with the whole dilemma of "Will Chomper turn on us?" Heck, even LBT 13 with the dinosaurs searching for Berry Valley, which parallels their original Great Valley journey from the first film. I could go on and on, but there's plenty of examples.
In particular I noticed that the concept of death is never really explored again, at least not to the same capacity. Certainly nothing like some of the gut-wrenching scenes we got in the original film. Aside from the occasional Sharptooth getting defeated, seeing the odd skeleton littered around, or the one-off flashback to Pterano's doomed herd, there were no more character deaths. Littlefoot's mother herself is seldom brought up. It's not that I feel characters needed to die off constantly, but at the same time I think there was some missed story potential there, and it could've made aspects of the sequels more intense and emotional. Especially because there are odd implications here and there; as Malte said earlier, cases of disappearing relatives, like with Cera's mother.
It's also an unfortunate symptom of why most of the Sharpteeth in the sequels didn't feel all that threatening or dangerous; after a while you just know that they're not really going to accomplish anything.
As for the songs, I don't think they needed to be taken out entirely, but I do think there could've been a bit less of them, or that they could've been made more serious and/or some of the sillier ones removed.