In retrospect, what was the point of the angels at all? The goal of NERV and etc. was the Human Instrumentality Project. Why go through the effort of killing fifteen angels? And even if you could say they had to establish peace for the moment to go ahead with the project, that just makes the entire plot of the angels a waste. So what was the point?
Note that, like many things in Evangelion, this answer would fall under the category of educated speculation.
The point of the Angels largely seems to be to drive other points of the plot. It seems that the plot of Instrumentality itself does not really need the Angels—and I think you're right in this respect. The Angels themselves are a Monster of the Week trope embodiment, but you'll notice that each one (except perhaps Matarael) has a large influence on the events of each episode (and often the whole series).
Consider Leliel, Arael, Armisael, and Kaworu. Each of these caused a great psychological trauma in the characters. Leliel was really the first to probe Shinji's mind and break him down to nothing; Arael and Armisael followed suit and brought forth even more trauma and, along with it, character development. Kaworu, the pinnacle of all of this, essentially brought Shinji to the verge of suicide, but then made his choices in The End of Evangelion all the more human and relatable.
The Angels also achieve one of Anno's goals of telling us that, well, humans are even worse. The fact that the Angels are actually just acting on instinct—the instinct to return to Lilith—and not actually destructive (with a couple exceptions) shows us that humans are really the strongest villains in the series. (A nice bit of grey area there.)
So, to answer your question: No, the Angels weren't strictly necessary. But the plot points they drove and the scenarios they created were critically important parts of the series.
The Angels NERV fought were the Children of Adam, who sort to instigate the Third Impact to reclaim earth back from the Children of Lilith, the Lilin (Humans).
NERV's goal all along was the preservation of humanity so stopping the Angels falls along their goals, the Human Instrumentality Project was SEELE's secret goal to force the evolution of man though creating their own Third Impact that they could control, because the Human Instrumentality Committee oversaw NERV it was also NERV's Secret Goal.
SEELE couldn't let Adam's children instigate the Third Impact because then they couldn't control it themselves so destroying the angels as they appeared was needed to ensure that SEELE's could execute their plans without interference.
In addition to the above two answers, Ner/Seele had to wait until they discovered the lost Lance of Longinus in the Antartic Ocean before they could begin Instrumentality. This did not occur until after the Angels began appearing, so they were obliged to battle at least some of them!
There was clearly some need to delay enacting Third Impact and Instrumentality until after the final Angel was dispatched, probably at the order of the Dead Sea Scrolls (which is never explained), otherwise Nerv/Seele would have simply commenced it as soon as they had the Lance (Adam, Lilith and Rei were already in their possession). For some reason, Instrumentality was only likely to work if there were no other Angels alive to prevent it.