why is Eliza's lapse into cockney dialect not only acceptable, but admirable in this setting?

You don't explain what section of the book you're in or the present setting. Cockney would be acceptable (admirable) when used in its own setting. It would mark Eliza as being a part of a certain group....... The cockney dialect is defined as follows;

The cockney dialect is an English dialect spoken in the East End of London, although the area in which it is spoken has shrunk considerably. It is typically associated with working class citizens of London, who were called cockneys, and it contains several distinctive traits that are known to many English speakers, as the dialect is rather famous. Some students of linguistics have become concerned that the cockney dialect may fall out of spoken English, due to the influence of multicultural immigrants in London who have added their own regional slang and speech patterns to the dialect.

The term “cockney” comes from a Middle English word, cokenei, which means “city dweller.” It is probably derived from a medieval term referring to the runt of a litter or clutch of eggs, which was used pejoratively to refer to people living in the then crowded, disease ridden, and dirty cities. The distinctive accent of working class Londoners, especially those living in the East End, was remarked upon by observers as long ago as the 17th century.

The primary characteristics of cockney dialect include the dropping of the letter “H” from many words, the use of double negatives, contractions, and vowel shifts which drastically change the way words sound. In addition, many consonants or combinations are replaced with other sounds, as is the case in “frushes” for “thrushes.” In some cases, the final consonant of a word is also dropped, for example “ova” for “over.” Many of the traits of cockney speech suggest the lower classes to some observers; for example, the use of “me” to replace “my” in many sentences is usually associated with a less than perfect understanding of the English language.

One of the more unique aspects of cockney speech is cockney rhyming slang. Although rhyming slang is not used as extensively as some fanciful individuals might imagine, aspects of it are certainly used in daily speech. In cockney rhyming slang, a word is replaced with a phrase, usually containing a word which rhymes with the original word, for example “dog and bone” for “telephone.” Often, a word from the phrase is used as shorthand to refer to the initial word, as is the case with “porkies” for “lies,” derived from the rhyming slang “porkies and pies.”

Cockney speech can be extremely difficult to understand, especially for Americans, as it is littered with word replacements thanks to rhyming slang, cultural references, and shifts in vowels and consonants which can render words incomprehensible to the listener. Like other unique dialects, a thick cockney accent can seem almost like another language. Care should also be taken when attempting to mimic it, as the cockney dialect can be very slippery, especially when it comes to the use of rhyming slang, and native users may be confused or amused by the attempts of a non-native.