Hangouts does, but it's impossible to know if we're "supposed" to be using Hangouts. A year or so ago I received a pop-up in my Hangouts app that Google recommended I check out Messenger [0]. It also seems to be the currently recommended option [1] although I don't know why since, as you say, Hangouts can handle all those scenarios.
This has understandably led to no end of confusion among Fi/Voice users, including myself. [2][3][4][5]
Hangouts can't receive MMS without special support from your mobile operator. Operators such as T-Mobile and... Google Voice... have been known to insufficiently provide that support.
Okay, you can announce that everything is fine, but it just ain't so. I missed MMS messages on T-Mobile in 2016.
Google's suggested solution, besides twiddling cellular network settings and asking your friends to keep texting you until it works, is to stop using Hangouts [1].
I believe you, but it's something that isn't quite as easy to compare anymore. I have a friend with an iPhone on verizon that has missed MMS or found it delayed by days. GV is easier to blame usually since it's different than other services.
Yes, features have been removed that don't fit the repositioning of Hangouts as an enterprise messaging app, and bigger changes based on that repositioning have been signalled as coming soon.
This has understandably led to no end of confusion among Fi/Voice users, including myself. [2][3][4][5]
[0] http://www.techtimes.com/articles/128591/20160129/google-ret...
[1] https://support.google.com/fi/answer/6062495?p=fi_tips&rd=1&...
[2] https://productforums.google.com/forum/#!topic/project-fi/eg...
[3] https://productforums.google.com/forum/#!topic/project-fi/04...
[4] https://productforums.google.com/forum/#!topic/hangouts/AcKr...
[5] https://productforums.google.com/forum/#!topic/project-fi/cB...