You could have killed off every main character in this movie and found yourself nonplussed because the characters really had nothing to attach you to them. The only one who had any depth was Kylo.
I liked Rey, Finn and Poe plenty. I find them very likable. Rey is very sweet, as is Finn. They're polite and caring characters. Poe is just cool as shit, so I can like the dude on those merits. However, what you're saying, I think, ultimately isn't terribly fair and I think your perception of Han's death is off. It's fine for you to have that opinion, but if I may-- yes, we care about Han mostly because of the previous three episodes. But that's the thing; he had three episodes worth of character development. I would argue, though, that Episode VI doesn't really develop his character too much. Han pretty much reaches the tip of his arc in Episode V.
What's not fair to me in this case is that we've only had one film with the new characters, so of course they're not going to immediately have the impact of Han's death, if one of them were to die in Episode VII. But they didn't, and they have at least two more films worth of development. What I appreciate about Han's death is that, again, I felt that he didn't get much, if any development at all in Return of the Jedi. His character peaked in Empire, full-stop. What Force Awakens does is throw something interesting for him into the mix: his son. We learn they're estranged, but Han still very much cares about him. Kylo cares about Han as well, deep down I think, but he's clouded by the dark side and is being torn in like a thousand different directions. I didn't get the sense that he wanted to kill Han, but he's under the scrutiny of Snoke.
What The Force Awakens did for me in terms of Han's character was finally give him one last oomph of character development before his sendoff, and I found it emotionally resonant. Han didn't just die-- his death directly contributed to a pivotal piece of development for our new villain. It wasn't a pointless, throwaway death at all. What I expected the new trilogy to do was to introduce a new set of characters that will be the real flesh and blood of the new story, while the older characters contribute in some way to their development. Han contributes to Kylo Ren. Luke contributes to Rey and her destiny. We've yet to see how the Luke thing plays out, but I have confidence that they'll find something very poignant to do, ultimately, with his character.
As for Finn, again, two full movies to go. This was absolutely the introductory episode for these characters, and I don't feel like I should judge their entire character arc based on what is the equivalent of the first act of three. I wasn't upset with Han's death just because I was very familiar with him, or because he's an iconic character that I've known most of my life. Surely the impact is helped by that, but I found it more tragic because of the reason behind his death. In any narrative with a villain, I think it's important that the villain does something absolutely heinous to get the audience to root against him. For Kylo, this was killing Han Solo. For Han's character, Episode VI left things pretty hunky-dory for Han and Leia. I didn't really care for that. I recall Kasdan and Ford both talking about how they tried to get Han killed off in VI, because there's really not much else for him to do.
Instead, they used it for VII, without Lucas being around to disregard the idea and finally do something with that character. It just felt right-- it gave Han more detail, it made sense, it established an emotional connection between Han and the characters, and again was very pivotal to Kylo Ren's character as our new villain. It served several purposes.
edit: apologies for the length of this post, I'm sure it could've been written more efficiently, but I like getting into the nitty gritty of things and sometimes that's not always so clear-cut and simple to explain. I'm not asking for some huge rebuttal of what I've just said, this is just how I saw things personally.
I do agree with you that Kylo had absolutely boss character writing in this. He's by far the most interesting villain for me so far in the series. Vader is obviously iconic and amazing, but relative to ANH and TFA, Kylo runs circles around him as a character, and this is also because of Han.