Learn English – Is using “while” instead of “whereas” discouraged in academic writing

"Phrasal verbs" are very common in English and have been around for a long time. Some are very old, some are recent inventions. Each has its own history and usage.

• Some of them are entirely acceptable in all registers:

  ^okAristotle refers to the effect of ethos and pathos on an audience.
  ^okI'm pretty sure that SOB was referring to me when he said that.

• Some are better used only in conversational registers:

  ^okPaul's always sounding off about how immigrants should be sent back where they come from.
  ^noIn his closing speech to the 20th Congress of the Soviet Union First Secretary Nikita Khrushchev shocked the delegates by sounding off for four hours on Stalin's reprehensible influence on foreign policy, the conduct of the war, agriculture, and civil society.

• And some are found almost exclusively in formal registers.

  ^okCopyright protection subsists in original works of authorship fixed in any tangible medium of expression.
  ^noJohn's folks subsist in the Ozarks.

There's no way of predicting which ones work where; you have to learn each one independently.

In spite of is not an idiom but a prepositional phrase. To alter (something) beyond recognition is just one of usage of the verb alter. They shold not be classified as idioms because of the following reasons:

Idiom is defined in Merriam-Webster as:

1. an expression that cannot be understood from the meanings of its separate words but that has a separate meaning of its own

2. a form of a language that is spoken in a particular area and that uses some of its own words, grammar, and pronunciations

3. a style or form of expression that is characteristic of a particular person, type of art, etc.

Idiom is a very-well known word, but some people don't understand what it exactly means. According to the definitions above, those expressions/forms of language/styles and forms of expression should not be written in a formal statement.

However, when it comes to mean in a broader way:

a common word or phrase with a culturally understood meaning that differs from what its composite words' denotations would suggest.

It can be used in a formal statement. They are broadly used by many politicians and businessmen.

Here is a list of English idioms in Wikipedia. You will find many of them are very familiar to you and useful. And you will clearly see how the listed idioms are different from in spite of and to alter (something) beyond recognition.