The phrase "a realization that should" is correct and usable in written English.
It can be used when discussing an understanding or insight that is expected to lead to a certain action or conclusion.
Example: "After much contemplation, I had a realization that should change the way I approach my work."
Alternatives: "an understanding that ought to" or "an insight that must".
It's a realization that could, and in my opinion should, remake the way we play the game of life, by inspiring us to make better lifestyle choices.
What developed later was a realization that they should be used for performance".
He said the effort entailed the extensive use of Arabic translators, as there was a realization that the Americans should not rely too heavily on Iraqi officials just because they speak English.
He said his view of Judge Rakoff's ruling was that "we should be more modest about our belief about what we have done when we have sentenced somebody to death, and that modesty should include a realization that we may well be wrong, which means we should be more open to reconsidering it, and we should not make it impossible to reconsider it".
Not unlike those who have been in an abusive or co-dependent relationship they have a realization that bullying is not and never should be the acceptable norm.
Other parts of the country are waking up to the realization that fresh, clean water is a scarce resource that should be conserved with wisdom and care.
In all this, the sad realization, and here's that gut check that should signal a compromise of integrity or ethics, the very funding many individuals and organizations are allotted is predicated upon deficit model thinking where those being served are viewed first and most prominently as victims.
It is, in other words, the state of affairs whose "realization" (bhāvanā) is expressed by the verb that should be judged predominant particularly in the injunctive sentences that represent, for Mīmāṃakas, the most important parts of the Vedas.
