A lot of what happens in the end and in episode 7 is meant to be set up for the next season. I'm gonna assume that after so many spoiler posts, people who haven't watched the show yet aren't clicking into this thread.
Kali's gang are absolutely going to come to town next season and they'll most likely be antagonists for the beginning half until the Mind Flayer makes another move. It tried to take over El when she was closing the gate, but she overpowered it, so I wouldn't be surprised if somehow Kali inadvertently finds a way to it or vice versa and she gets taken over, but that's just a guess.
El snubbing Max is a good sign that she's marking her territory more or less. She's always been more instinct than person, it's why there's such a heavy parallel between her and the Demogorgon in season 1. She acknowledges that the gate is her fault, that all of this was her fault, but she doesn't know how to say that, so she just says that she's the monster. It's that inability to communicate heavily and a focus on the instinct that she knows well which causes her to act as though Mike is hers (which he totally is) and that anyone who could potentially come between them is maybe not an enemy, but not a friend, not in the way she knows a friend to be. I'm sure things will cool down when she realizes Mike isn't interested in Max at all, but it was necessary for Max to be in the group for El to feel somewhat challenged in her place and become jealous. The whole season, for El at least, was about her being challenged to grow up and realize just how much potential she has while also maturing into more than just the instinctual monster. Dealing with her family life, realizing it's more complicated than she knew with her sister, putting Mama to "rest" so to speak, all points to her settling down in her place as Hop's daughter, Mike's girlfriend, the party's Mage, and the de facto head of the group when she needs to be. Maybe not a leader, but a boss ass bitch for sure.
Without Max, that element wouldn't have been there as heavily because El wouldn't have needed to be jealous over anything. That's not to say that it's literally all because of Max, but it is one puzzle piece that fits into things and makes things work properly.
As for Billy, I do feel that he should have been more involved in things to give him more of a purpose, but having an antagonist that's still human and facing human issues entirely unrelated to the mind flayer or demodogs is a good way of keeping the show grounded. "Remember to plant your feet." He's there to ground the story in the actually important issues going on while all of the paranormal stuff is happening too. Sadly, he could have done all of this while still also becoming involved in the paranormal stuff. Had he chased them into the tunnels or something and then seen the demodogs and realized holy shit, something is not right and my sister is involved in it big time, it would have left him at an important crossroads for season 3 if whether or not he actually cares about her, whether or not to get more involved with that side of things like Steve did at the end of season 1, and it would have given more footing to him being the evil side of normalcy, the antagonist who, while still being an asshole who doesn't want or need to be redeemed, serves a specific, clear purpose of grounding the audience and the main characters alike. It would show that life doesn't stop just because monsters attack the town.
With Billy, they didn't completely drop the ball, they just didn't succeed with him entirely or, better put, they didn't go as far with him as they should have. Taking the evil of normalcy all the way into the tunnels and having the two separate evils acknowledge each's existence would have been top notch, mostly because we'd get a totally human reaction to the demodogs and the tunnels while also getting another look at the paranormal reacting to someone who knows literally nothing about what they're walking into. We got a little of that with Max, but everyone else has some measure of experience with stuff like this now and they told Max all about last season. Bob was also all about helping Joyce, so his gung ho nature is somewhat motivated by that. It's not a pure reaction to what's going on, not entirely. Billy is one of the only human characters who could have reacted to the paranormal in a way that would have given a different angle on things, someone who has enough shit on their plate that doesn't want to get involved with "whatever the fuck is going on."
And I ended up making a huge post, fuck. Suffice it to say, I think Max and Billy served their purposes, but while Max was done well and served the right amount of purpose, Billy did not or at least not enough. They could have used both of them more effectively, but I think what we did get wasn't inherently bad or flawed, it just wasn't enough good stuff.