Help with specific usage of 'Should'

The RSC Shakespeare Complete Works page 20:

Thus the boy Shakespeare might have been asked to imagine that he was wise old Nestor ‘exhorting Achilles by letter, that he bear bravely the snatching away of Briseida by Agamemnon, showing that one must bear even with an evil ruler, and public good must be preferred to private grief’ or – being asked to inhabit the opposing side in the Trojan war – to write in the voice of Antenor persuading King Priam ‘that he should not be unwilling to return the stolen Helen to her Menelaus, either because it was just in itself, or because it would be the part of a very foolish ruler on account of the most shameful love of an effeminate youth and hardly a man Paris to cause that so many very brave men should enter battle’.

My question is in regard to the last "should". What does it mean, or what definition it is referring?

I'd say that this is an example of 'emotional should' as Otto Jespersen terms it. The men did enter battle, and so this version of 'should' is there to emphasize the disagreeability of this fact, that this was a pointless waste of these men's lives.

Emotional should.

20.5(1). Should is very often used in passing a judgment of an emotional character (agreeable or disagreeable surprise, indignation, joy) on some occurrence; whether this is a fact (something which is happening or has happened) is neither indicated nor denied by the form of the expression, but is left to be concluded from the context or situation; as a matter of fact this mode of expression is of frequent occurrence in giving one's opinion of an actual fact

More U 60 I thynke it not right that the losse of money should cause the losse of mans lyfe | Sh H4B 11. 2.42 it is not meet, that I should be sad now my father is sicke | Lr 11. 4.1 'Tis strange that they should so depart from home. And not send back my messengers I A V Gen 2~18 It is not good that the man should be alone | Spect 182 Is it not wonderful, that the love of the parent should be so violent while it lasts; and that it should last no longer than is necessary for the pre- servation of the young? | Austen P 8 It is such a good joke, too, that you should have gone this morning, and never said a word about it till now | Shelley L 528 I accuse myself that my precipitancy should have given you the vexation you express | Macaulay H 1.48 It ia not strange,. therefore, that the Tudors should have been able to exercise a great influence | Tback E 2.148 'tis a marvel to think that her mother was the poorest and simplest woman in the world, and that this girl should have been born from her | Bronte V 244 That I should dare to remain thus alone in the darkness, showed that my nerves were regaining a healthy tone | Di Do 112 I thought it well that you should be told this from the best authority | id D 255 It's natural and rational that you should like it | Doyle S 1.203 my father went from home . . . I was glad that he should go | Barrie M 17 I'm ashamed you should have me for a mother.

"It is strange that he exercised (or, has exercised) 80 great influence" merely states the fact; "it is strange that he should exercise 80 great influence" (cf. the quo- tation from Macaulay) lays more stress on the strangeness by using the imaginative should in the clause. In the quotation from Thackeray the marvel is not that the mother was poor, but that such a woman could have such a child.

(Jespersen. Modern English Grammar. IV)