You're right that Vol. 2 had a very different line-up, but I also believe that a lot of that had to do with the circumstances of the time. They were fresh off of Children's Crusade, which means that two Young Avengers were dead and couldn't be used. Eli also couldn't be used due to his weird legal status at the time (which is why Gillen used America instead, according to his own word). It wouldn't make sense to use Nate, considering how he literally murdered one of the members. So Tommy was the only available character that Gillen intentionally left out of the main roster, and even then he found a way to add him to the story in the middle and end.
Now flashforward to 2019/2020, the most recent time that we had Young Avengers reunions, and most classic members (except for Nate and Jonas) were used. I feel like if we had a relaunch right now, it would be a lot more likely to see a more classic line-up (albeit with a few additions like America and/or whoever else they might wanna add to the team). I find it hard to believe they would leave Cassie, Eli and Tommy out, specially when all of them are in the MCU already.
As for Billy and Teddy, honestly... I don't think it makes that much of a difference. Their status quo had no influence over Billy appearing in Trial Of Magneto, and their most recent digital book literally suggested that they would split their time between Earth and Space. I think Marvel can just relaunch Young Avengers and say that this is what they do when they're not busy with space. I don't think most fans would care as long as we get Wickling content.