It seems to be a direct quote from Bible. It probably IS correct, albeit in somewhat archaic English.

Should is used here to convey the subjunctive mood (虚拟语气) but: 1) the subjunctive forms are used less and less often in English these days (it is still very common in some other European languages, especially Spanish) 2) even when the subjunctive was more common, using "should" to convey it was only common in British English So it's not surprising that you came across it in a translation of the bible, and I'd surprised if it wasn't a British translation rather than an American one.

Deleted so I can make it an answer not a comment

I think you have caught it correctly. The English implies repetition of the previous part. It’s better for you that they should fail .... than that you should (fail ....) It’s better for you that they should fail .... than that you should (fail) . It's better that they should pay than you should. Using "should" in this way is a little old, but ok. It's easier for her that you should do the heavy work than she should. . Translations of texts such as you have, tend to vary inm the degree to which they change the wording. Some modernise completely, some amplify, some try to keep an air of old as if written long ago as feeling more authentic. Natural modern language may or may not be the best aligned with your aim. . It is better that you do the hard work of translation than every reader should (have to). :)