Why do people use ‘should’ in “It’s funny you should say that”?

I’m a bit astonished about this special use of should:

1. (It’s) funny you should say that.

What explanation is there for using should in that expression?

I think there would be no difference in sense if it were rewritten without that should, as in:

2. Funny that you say that.

Is the second variant, the one without the should before say, also used?

If this second variant without should does actually exist, then does it always mean the same thing as the should version means or can the hypothetical second variant ever mean something slightly different?

'Should' sometimes appear to carry the idea of 'happen by chance''.

If you see Fred tomorrow, please give him my regards. / If you should see Fred tomorrow, please give him my regards.

It's odd/strange/interesting (that) you say that. / It's odd/strange/interesting (that) you should say that.

It was odd/strange/interesting (that) you said that. / It was odd/strange/interesting (that) you should say that / should have said that.

The utterances with 'should' are more tentative than those without.

Lexico's definition of "should" says:

Used in a clause with ‘that’ after a main clause describing feelings.

• ‘it is astonishing that we should find violence here’

• ‘It seems to me revealing that Mr Halley and Mr Gibbins should describe him as if he were one and knew what he was doing.’

• ‘I am astonished that you should take exception to an obviously Platonic enthusiasm.’

• ‘He was so anxious that she should like them and they her.’

• ‘It is shocking that we should pay many times more for the care of criminals than we do for the care of children with special needs.’

I don't think there's any tentativeness to it, but usages besides "it's funny you should say that" sound a bit quaint to my American ear.

If we con­sider, slightly more for­mally:

• It is sur­pris­ing that you should say that.

And then start sub­sti­tut­ing sur­pris­ing with other ad­jec­tives, then it seems more nat­u­ral, such as for ex­am­ple:

• It is in­cred­i­ble that you should say that.

I be­lieve that should here is a modal aux­il­iary ex­press­ing a sub­junc­tive mood, al­though oth­ers may dis­agree.