Picture but no name wouldn't work because many people don't have pictures for all of their contacts, and of course won't have for incoming calls from people not in their contacts list or one-off people they call from the mobile. So you need the name or number (just showing these where there is no picture would just look plain odd).
Personally I don't find "Picture of Tammy, missed call from, name Tammy" confusing at all, because it's my phone's call log not Tammy's so of course the call was between Tammy and me. The only possible ambiguity is whether it was an incoming or outgoing call, and that, on most apps, could be clearer.
So as for arrows vs text, yes, text will always be clearer. But text only works if you have a separate entry in the call log for each call, or at least separate entries for incoming and outgoing calls. The phone app is one of the apps that most manufacturers include their own version of, so varies a lot between devices, but all of my recent phones have combined entries, so one entry in the log shows multiple calls to & from the same person if they were made the same day. So you could do that, but it would use up more space in your call log display, which is one of the choices developers must make: space vs information? This is the biggest weakness of my Pixel's phone app: for example I can see that I had multiple calls with my daughter yesterday, some successful, some missed, but no more information than that. Personally I'd like to have the option of a more detailed display, and some of my previous phones have offered more.
Colours are actually bad design: red/green colour blindness is the commonest type, and affects a significant fraction of people (most commonly males). It might provide an extra cue if you have words (where it's intelligible anyway), but colour by itself should never be relied on.
Anyway, it's an interesting discussion, but you really need to raise it with the phone manufacturers, or Google for the Pixel models. This is a discussion forum for users, and so we've no ability to change the design of these apps.