It is a matter of the verb. ) in the main clause, where yours seem to be simply reporting verbs. The putative 'should' is primarily a BrE device, and I don't know whether your 'should's are included in that term.
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cho7712All above five sentences do not permit the omission of 'should' so that present subjunctive is impossible.So why is that?As Mr. M. says, they have the wrong kind of verb for "evaluative" should. Therefore, the should that you see there is not "evaluative" should, but "advice" should. Thus,
cho7712As to the use of 'should' in that-clause, it is generally known that the bare infinitive without 'should' is just the variant form. [...] + bare infinitivecho7712And I found that the form without 'should' is called the present subjunctive.It just happens that the present subjunctive form of all verbs, including BE, has the same form as the