In British English, acquaint is very formal. As this NGram graph shows, its usage peaked about 1820 and fell rapidly till 1900: since then its usage has continued to decline.
Looking at actual instances of its use both in the 1820's and in modern times, it is typically used more for acquiring information that for getting to know a person.
Schmidhuber acquainted Michael with Albert.
This sentence is grammatically correct and understandable, however it is not at all natural in current usage. The introduce version is more current.
I would generally only use acquaint in a formal, written document, and only when it concerns familiarisation with ideas. For example:
We acquainted ourselves with Fechner's scientific realism by looking at atomism. - "Nature from Within: Gustav Theodor Fechner and His Psychophysical Worldview", Michael Heidelberger
One exception which refers to people is the stock phrase "to get acquainted". for example:
At this point, it would be appropriate to introduce the new employee to the chosen mentor and allow time for the two to get acquainted - New Employee Orientation Training, Karen Lawson
Alternatively, the event may be seen as positive if the other party is a woman the man finds attractive and he views the incident as an opportunity for the two to get acquainted - Encyclopedia of Behavior Modification and Cognitive Behavior, Michael Hersen
Having introduced two people, you can use this stock phrase in speech, and it does not sound too pompous:
Mackall stepped forward, shook Norton's hand and headed for the door. “I will leave you two to get acquainted.” - For Love or Honor Bound, Derek Hart
It is easier to say "get acquainted" than say "get to know one another" (four syllables rather than seven), and the latter is a bit too informal for some people. This NGram graph shows that, despite its clumsiness, the informal "get to know one another" is gaining ground.