You’re right, in southern British English one might say “Shall we go to the match tonight” meaning “Do you fancy going to the match tonight”, so it’s not a substitute for will as it has a different meaning. That usage is in my experience quite common and used in informal speech. This is one of these cases where an archaic word or construction has to all intents and purposes ceased to exist, except in a few standardised use cases. I would call it a linguistic fossil for want of a better term.
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Also, might come in handy when you’re a Gandalf, say, at some private club’s entrance and you ain’t gonna let some Balrog in.
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I would say that qualifies as extremely formal and archaic in its usage 
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…or an English teacher while handing out exam sheets 
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The correction of the first sentence has gone awry.
The corrector has failed to correct the preposition “at” and optionally corrected “will” giving an erroneous explanation, as
Use of “will” and “shall” according to the British English dictionary:
We use “will” for all persons, but we often use “shall” with “I” and “we”. “Will” or “I’ll” is generally less formal than “shall” when used with “I “ and “we”.
Example sentences with “shall”
• Simply complete the form and return it to me, and I shall personally reserve your hotel room for you.
• We shall look at a full report from the centre.
• We’ll see you in the morning.
Shall also has a special legal use
… for talking about rules and laws. In these cases, we often use it with third-person subjects:
According to the basic principle of human rights, people shall not be discriminated against because of their nationality, race, age, sex, religion, occupation and social status.
Shall and will are both used to talk about intentions and decisions. Shall is more formal than will.
I’ll see you later. I won’t be late.|informal|
|I shall see you later. I shan’t be late.|formal|
Will is much more common than shall in both speaking and writing.
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Thank you @Maria2 for your useful insights as usual.
Seeing the shall is definitely more formal and based on the answers, I have the feeling that Americans, that have the tendency to be more informal, have relegated shall to the legal aspect only and in other few limited occasions (that somehow becomes funny, ironic or satiric because they leverage the formality of shall in contrast with the situation they are living).
Rather than in UK or maybe other part of the world that have more areas where a part of people have the tendency to be more formal, including televisions and written media, they somehow keep shall alive in more situations.
Does it make sense?
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The correction should have been:
Tomorrow I will be flying to the United States, to the City of Los Angeles.
On Tuesday I will attend an event there.
Explanation:
“I” should always be capitalized.
This country is called “the United States” and not “United States.”
You never fly “at” a place unless you are attacking it. We fly “to” Los Angeles.
We are never “on” an event, but “at” an event. Or, more commonly, we “attend” an event.
“event” is not capitalized. It’s not a proper noun.
“event” begins with a vowel, so we use “an” instead of “a” for the preceding article.
Cheers.
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In modern English, the only time you would use “shall” in daily conversation is when you are being very polite and asking if you “shall” do something for someone.
I.e. “Shall I take your jacket?”
I am an American trial judge. Shall is always used in legal text to convey some action or thing is mandatory .For ,example , all operators of motor vehicles on public roads and highway shall obey the posted speed limits.
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