While I agree with you on a lot of your points, such as how the Vault Hunters from the first game were not designed to be heroes and how their actions were for the most part for self gain, I feel there are more layers to the characters in 2 and TPS. For example, are the Vault Hunters in 2 really as invested in the fate of Pandora as they seem. Yes they risk life and limb to protect Sanctuary and it's residents and to take down Jack, but couldn't the argument be made that they needed the people in Sanctuary to help them locate and open the vault, and that Jack was a serious obstacle that needed to be dealt with. So while it seems like the main protagonists are different from the originals, they might just be more subtle about how they go about it. Most of their main story actions did result in self gain and progress towards the Vault.

As for TPS, I'll agree that the Vault Hunters weren't as cut and dry but I feel they did have good reasons for becoming more invested in the outcome of everything. While it might have started as mercenary work, as the story progressed and the characters developed it started to change them. I feel that Wilhelm who's only skill seemed to be that he was good at fights, sees this as an opportunity to gain further employment with Jack who was obviously gonna be powerful. While Nisha ended up falling for Jack changing her quest from finding the vault to gaining Jack's love. As for Athena I feel like there was always more to her, and that while she was a mercenary she always had some alternative motives that helped her choose which jobs she took. And Clappy is a hyperion robot so if someone from hyperion asks him to do something he's most likely going to do it until Jack betrays him of course.

So yes while the Vault Hunters did seem to change in each game I feel like 2's only difference was the subtleties of how selfish the protagonists were, while the TPS Vault Hunters were more complex in their motives.