IUPAC Nomenclature of Cumene
Let me abstract your question to “Why is the $\style{font-weight:bold}{\ce{-CH(CH3)2}}$ group sometimes named ‘isopropyl’ but almost never ‘sec-propyl’?”

iso alkyls

‘Iso’, obviously as in ‘isomer’, in IUPAC organic nomenclature (last one is from 2013) evolved to non-preferred, retained names for several smaller alkyls, that are linear but specific single branching at the carbon next to the terminal carbon, by additional methyl.

These are (intentionally skipping our dour discussed $\ce{C3}$ branched alkyl):


isobutyl &nbsp;&nbsp; $\ce{-CH2-CH(CH3)2}$
isopentyl &nbsp; $\ce{-CH2-CH2-CH(CH3)2}$
(isohexyl &nbsp;&nbsp; $\ce{-CH2-CH2-CH2-CH(CH3)2}$ &nbsp;, only in old IUPAC 1979 nomenclature, see here)


(However, in general naming of bulk chemical products, larger alkyls with different branching are named isoalkyl, e.g. ‘isooctyl’ $\ce{-CH2-CH(CH2CH3)-CH2-CH2-CH2-CH3}$.)

sec- alkyls

Obviously ‘sec-’ is for 'secondary’, meaning there's a branching into 2 carbons at the first carbon atom. The list of retained names has only one item:


sec-butyl $\ce{-CH(CH3)-CH2-CH3}$


but our candidate would fit in here as well.

Why only sec-butyl? A major reason could be that the next “sec-pentyl” would represent two different structures:


$\ce{-CH(CH3)-CH2-CH2-CH3}$
or $\ce{-CH(CH2CH3)2}$ ?


(Now one might ask, why there is not some naming system for alkyls with methyl branch at the first atom, similar to iso alkyls with the branching at the next-to-last carbon. I don't know.)

Why not sec-propyl? The $\ce{-CH(CH3)2}$ is a special case that can fall into both isoalkyl and sec-alkyl class. The better defined one, also resulting with simpler spoken name and simpler typography (no dash and italic) – isoalkyl, was once chosen. That's my humble hypothesis.

(And please note that the preferred IUPAC name for this group is propan-2-yl. Alternate name is 1-methylethyl. Isopropyl is still retained.)