I've been told that this sentence is describing the size of the mask being half the size of the face, Can't we simply say 「顔の大きさの半分であろう大きなマスク」 instead?
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This type of は means "at least". That is, the mask covers roughly 55-70% of the area of the face.
The sentence can be rephrased as 顔の大きさの半分はありそうな大きなマスク, 顔の大きさの半分以上あるであろう大きなマスク, etc. But 顔の大きさの半分であろう大きなマスク does not have the same meaning.
While you probably already know this, [であろう] is a literary/formal way of saying だろう/でしょう. It should not be separated into で and あろう any more than でしょう should be separated into で and しょう.
Let's rephrase the quote in question:
Maybe it is easier to see now how the でしょう relates to the clause [顔の大きさの半分はある], or 'The mask was as large as half the size of a face.'. The end result (including でしょう) is a sentence more equivalent to '____ probably as large as half the size of a face.'.
The はある expression would, in English, be stated as 'there exists/existed', or 'it is/was'.
If you search for 「はあるでしょう」or 「はあるだろう」, there are many results. On Kotonoha alone, there are over 400 combined examples. If you change the particle は to も, there are over 1000 combined results.
Just to pick one out of the results:
「そんな経験が 誰にも 一度はある だろう。」 'That type of experience, for everyone there probably exists that one time.', or more colloquially, 'Everyone has probably had that type of experience.'
Now, to remove the であろう expression entirely. Again, Kotonoha has over 1300 results for 「はある。」. Here is one:
一度見る価値 はある。'It is worth seeing once.'
From the above sentence and how it relates to your main question, I hope that you can see that はある helps to complete (round out) a clause.