The phrase "admonition should" is correct and usable in written English.
It can be used when discussing the necessity or recommendation of a warning or cautionary advice.
Example: "The admonition should serve as a reminder to always prioritize safety in the workplace."
Alternatives: "warning ought to" or "caution must".
However, a longish period of education and gentle admonition should inculcate the habit of eating three meals a day, indoors, sitting at a table, no matter how strange it seems at first.
Perhaps Ike's admonition should be updated then to read "In the councils of government, we must guard against the acquisition of unwarranted influence, whether sought or unsought, by the political-industrial complex".
Respondents, especially men ages 18 to 35, the elderly, and people in lower socioeconomic groups said that dietary admonitions "should be taken with a grain of salt".
It is an admonition that should be taken with a grain of salt, said Chris Petrillo, a product manager at the company.
Collins doesn't recall ever seeing a Bible among the books in his parents' house, and the only time they sent him to church it was for the choir music, and with the admonition "You should be respectful of what they're doing, even if the stuff they're talking about doesn't make a lot of sense".
Sor Juana's "Respuesta a sor Filotea" (1691, "Reply to Sister Philothea") displayed her erudition in defense of her intellectual passion, arguing that St .Paul's often-quoted admonition that women should keep silent in church (mulieres in ecclesia taceant), should not prohibit women's pursuit of knowledge and instruction of young girls.
The last named is the source of her often-quoted admonition that poets should present imaginary gardens with real toads in them.
The team's victory was a reminder that something had been saved and built upon in the Gulf, and an admonition that it shouldn't be lost again.
Every seven weeks, for restoration he runs only once a day instead of twice, an allusion to Exodus 23:11 and the admonition that farmers should leave their fields fallow every seventh year.
"As a young guy, I was totally hooked on 'Elektra,"' Mr. Welser-Möst said, recalling Herbert von Karajan's admonition that one should not conduct the opera after age 60 because of the risk of a heart attack during the final pages.
I was reminded of Arthur Sackler's admonition that you should endeavor to leave the world a better place than it was when you came into it, and I wondered about the moral arithmetic of the Sacklers' deeds.
