When a noun followed by a restrictive clause is preceded by "whichever" or "whatever", it is incorrect to introduce the clause with *that*

When a noun followed by a restrictive clause is preceded by whichever
or whatever, it is incorrect to introduce the clause with that in
formal writing: Whatever book you want to look at will be sent to
your office or Whichever book costs less is fine with us.

https://ahdictionary.com/word/search.html?q=whatever

What are the grammatical reasons for this?