A.R. Burn,
Persia and the Greeks: The Defense of the West, 546-478 B.C. (1962; rpt. Minerva Press, 1968), p. 350:
No Greek city really liked placing its forces under the command of an ally; indeed, no Greek really liked placing himself under another's orders at all; Athenian discipline, it has been said, was 'such as one might expect in a place where "to obey" was the same as "to be persuaded"'.
The Cambridge Greek Lexicon, Vol. II: Κ-Ω (Cambridge: Cambridge University Press, 2021), p. 1098, s.v.
πείθω:
1 win over (someone) to an act or course of action (esp. by
speech or entreaty, oft. opp. compulsion or deception); win
over, prevail upon, persuade —persons, their heart or mind...
[....]
4 || MID.PASS. (also ep.fut.) let oneself be won over (so as to
obey); be persuaded, comply ...; comply with, obey...