May I say that

Hello guys

You English speakers often say "may I say" when you make a speech, as shown in the example below.
"In conclusion, may I say that I hope others will be encouraged to undertake their own study of the schedules"

My questions are:
(1) Why you invert "I may say" into "may I say" despite the fact you are making an assertive statement?
(2) What do you mean by this "may I say"? Could you paraphrase it into other words?

Thank you in advance

If you use the uninverted word order, "I may say", then it sounds as if you're uncertain about your statement. ("I may say it, or I may not.")

When the order is inverted, the phrase carries a different meaning. It's equivalent to, "Let me say..." or "I'd like to say..." It's just a formal way of introducing your statement. It can be interpreted as a ceremonial way of showing deference to your audience, as if to say, "If it pleases you..."

It's inverted because it's actually an interrogative -- may I say ....? It's just that it's such a common rhetorical phrase that the rest of the sentence tends to not end on a rising note or even get treated as a question, but that's actually how the phrase is technically read.

May I say that I'd agree with both Lazar and Uriel? I don't expect a "No, you may not." and in any case I've effectively had my say on the matter.

Yes, a fossilized question. = "please permit me to say"