By the time I posted this (in an incomplete state, though it's done now) others had also solved the first 5 clues. I shan't reproduce those solutions here. Here are the last three.
Arctan maps every other arccot into an embankment, too (8)
ABUNDANT. (Take the word ARCTAN. Replace RCT, found as alternate letters of ARCCOT, with BUND, a type of embankment. Then add T, which I guess comes from "too" in the clue though I don't quite understand how.)
Heated rant with part of Ulam spiral (7)
NATURAL. (Anagram of RANT ULA).
Curse without Germain’s initial initial (4)
PELL. (SPELL without the initial letter Sophie Germain's first, i.e., initial, name.)
So, what's next? Well,
all the answers are names of particular sets/sequences of integers, and the question directs us to OEIS. And of course we have those italicized words. I confess that before doing what I'm about to describe I tried a couple of other things that incorporated most of the right ideas "but not necessarily in the right order"; a helpful hint from OP in the comments set me on the right track. So: take the position of the italicized word in each clue, and use it to index into the corresponding sequence of numbers. In some cases there's more than one possible convention as to where to start; following the advice in the puzzle we'll use the version in OEIS. We get (SQUARE:4) 9, (CATALAN:5) 14, (TETRAHEDRAL:5) 20, (FIBONACCI:6) 5, (PRIME:4) 7, (ABUNDANT:2) 18, (NATURAL:1) 1, (PELL:5) 12, mapping via A1Z26 to letters I N T E G R A L.
So clearly the answer is, appropriately enough, that
mathematics is integral to our daily lives.