Singing: American r

The reason has to do with articulation and sonority. The American
retroflex r pushes the root of the tongue back into the throat cavity,
which is the largest resonator in the vocal tract. This constricts
the throat cavity and reduces sonority, which, in choir director
terms, damps the sound. Choir directors and voice coaches don't like
sounds that do that, hence the r-lessness of good choirs and singers,
including Motown.

Herb Stahlke from ADS-L

Why vocal exercises?

Google it, you can find tons of vocal exercises about speech and singing. They usually involve 5 prime vowels, with /g/, /m/, /n/, and /h/

nasals: m and n
glide: h
velar consonant: g

Why?

"Voice Production in singing and speaking" got an answer.

p.207

(1) The single sustained tone
(2) The tones of a scale sung so as to be smoothly linked together
(3) the same, sung somewhat more independently of each other
(4) the same, but each tone beginning and ending very suddenly
(5) the swell

All others are modifications of the above.

/m/ warmup: mah, mee, may, moh, moo

Many voice/singing teachers ask their students to practice garbage like m +{a,e,i,o,u}.

Why?

"/M/ warm up: To warm up the vocal cords the consonent M is spoken or sung before the words. This helps to produce a gentle air flow through the larynx as phonation begins."

pure vowels; consonants; singing

ay oh roundness,front/back
ee oo
ah

s,z: quick articulation (no more hisssing)
r: just dont pronounce it