Unjustifiably comes to mind: a reason is needed to justify an action. Or possibly perversely. Or unreasonably.
unjustifiable : Not able to be shown to be right or reasonable
perverse : Showing a deliberate and obstinate desire to behave in a way that is unreasonable or unacceptable
unreasonable : Not guided by or based on good sense
Oxford Dictionaries Online
However, without providing a reason doesn't mean that there isn't one and the ban cannot be justified.
I'm not sure what language you speak natively, but it's possible that your mother tongue has a more structured concept of formality that English does.
In English, formality is expressed in a number of ways. Here's a few I could think of (though there are certainly many more):
Contractions
Using contractions such as "can't" or "doesn't" is usually less formal than using their full forms (in this case "cannot" or "does not").
Word origin
Words of Latin origin are typically more formal than words of Germanic origin (for example, "assist" is more formal than "help", though they mean the same thing.
Sentence structure
Some sentences can sound more or less formal depending on where the subordinate clause is placed. For example:
"We couldn't see the mountains because of the fog."
"Because of the fog, we couldn't see the mountains."
The second, in addition to emphasizing the dependent clause more, sounds more formal.
Flourish
Sentences can sometimes be made more formal by adding words which aren't necessary to their meaning. This is common when making polite requests:
"Do you want to dance?"
"Would you be so kind as to do me the honor of dancing with me?"
The second is much more formal -- the request is "softened" by the addition of unnecessary words.
If anyone disagrees with what I've listed above, please leave a comment. One person's opinion is hardly fact.
Best Answer
Yes, this seems fine. The former is not attached to informal language whereas the latter can be.
To say 'from all over' is perfectly normal to describe what you have written under that context and it is not an informal phrase.
It's a way to express something or someone coming in from numerous directions, many different or varied places and so on and so forth.