Do we care about the rules of "Speculation Modals" when we change speculation modals from "direct into indirect speech"?

Question

According to the rules of "Speculation Modals", we use "may / could / might + inf" to guess things in the present

Eg: I may / might / could be late today

"Speculation Modals" say that we use "may / could / might + have + PP" to guess things in the past

Eg: I may / might / could have been late yesterday

According to the rules of "Indirect speech", we have to change "May--> might; could ---> could & might--> might" when we change from direct into indirect speech

Eg: David said "I may be late today"= David said he might be late yesterday (this statement is said 1 day later)

But the phrase "he might be late yesterday" broke the rules of "Speculation Modals". That is, to speculate a past event, we have to say "he might have been late yesterday"

I don't understand

Do we care about the rules of "Speculation Modals" when we change speculation modals from "direct into indirect speech"?

Answer 1

If I say

He said yesterday he might be late.

I am reporting what he said about an event which was in his future at the time of his words. He could have been on the road and due to meet with me at 2PM but traffic was going to delay him until 2:30. Or he could have been speaking about something which was scheduled for today or next week. Suffice to say, the event he was speaking about was in his future at the time.

If I say

He said yesterday he might have been late.

I am reporting what he said about an event that was in his past. He is trying to recall whether he had arrived on time or arrived late. There is a distinct possibility that he was not on time for that event.

Answer 2

Might, could, would are historically the past of _may, can, will. They sometimes get used in this way, especially in indirect speech, eg He said he could do it.

But in Modern English they are also independent modals with their own meanings, and in this use, they can be use in present or past, and they don't change in indirect speech. They are often more tentative, and used either for politeness, or to conceal real motives.

He said he could do it.

with no special emphasis on the "could", is simply the indirect form of He said "I can do it".

but

He said he could do it.

might be the same, but it might also be the indirect form of He said "I could do it".

where the "could" is more tentative, and might be implying that he didn't want to.