What is the point of 的 in '你也是大学生？你是什么专业的'?
The hidden noun that Chinese Grammar Wiki refers to is 大學生 (college student). They argue it is short for

你是什麼專業的大學生？

Which is kind of true. 什麼專業的 is adjectival on 大學生, specifying what kind of major the college student is (pursuing).
A better way to look at 是...的 according to its function (emphasis) is to just delete 是 and 的 and see if the rest makes sense on their own:
是...的 omission

(1.1) 你是什麼專業的？
(1.2) 你什麼專業？
(1.3) 我中文專業。

All of the above are grammatical. Sentences (1.1) and (1.2) mean semantically the same, except the former gives emphasis on 什麼專業 and has the nuance of courteousness.
In sentences (1.2) and (1.3), 什麼專業 and 中文專業 become adjectival nouns. They are placed after the noun as a verbless predicate, i.e. in the form of N+Adj., which can sometimes be a stand-alone sentence. Think of 你好嗎[吗], where the speaker greets the listener (literally) if the statement 你好 (lit. you good) is true (by the yes/no question particle 嗎). Adj+N, on the other hand, is the only correct way to position the adjective when we want to create a nominal phrase. So:
N+Adj. vs Adj+N

(2.1) 高個[个]子 tall stature
(2.2) (他)個子高。 lit. (His) stature is tall.
(2.3) 中文專業的我 I, a Chinese major

Only (2.2) is a sentence. (2.1) and (2.3) are only nominal phrases. 的 is required for pronouns (2.3). And now:

(3) 他個子是高的，不是矮的。 lit. His stature is tall, not short.

Sentence (3) emphasises the stature of the person the speaker is referring to. In that case, it would be hard to sensibly add any noun after 的. Perhaps 個子, as in 他個子是高的個子 (lit. his stature is a tall one), but that is very poor style of writing.
Finally,

(4) 他是我的。He is mine.

In certain occasions such as that of sentence (4), reduction into 他我* would not make any sense. Adding a dummy noun 東[东]西 (thing) then suffices, as in 他是我的東西, showing possession. Again that is for understanding, writing it would not be stylistic.
Whichever method (adding a dummy noun or deleting 是的) you choose is fine, as long as it makes sense.