Chopin always insisted upon smooth playing by his own pupils. He encouraged his students to attend or join choirs, operas so that they could understand a singers phrasing and expression. Bad phrasing on the piano in Chopin's mind was exactly like someone speaking in a language that he did not understand, a "speech" that he had been laboriously memorised.
Chopin to Karol Mikuli (Head of piano teaching at the Conservatoire in Lwów)
"The musician who phrases badly shows that music is not his mother-tongue, but something quite foreign and unintelligible to him."
So the idea of identifying a singing voice in Chopins piano music is very helpful and important to maintaining effective phrasing and smoothness of your playing.
Concerning Chopins "tempo rubato" Liszt said rather poetically,
"In his playing the great artist renders enchantingly that sort of emotional trepidation, timid or breathless, that seizes the heart when one believes oneself to be in the presence of supernatural beings..... He always made the melody undulate like a light boat borne on the bossom of a mighty billow, or else he would give it a wavering motion, like an aerial apparition suddenly arising in this tangible and palpable world. He indicates this in his compositions... by words tempo rubato: stolen, broken time, at once supple, abrupt and languishing... like a cornfield rippling under the soft pressure of a warm breeze, like tree-tops bent hither and thither at the whum of a capricious gust."
Mikuli's descrition is less poetic
"While the singing hand, either irresolutely lingering or, as in passionate speech, eagerly anticipating with a certain impatient vehemence, freed the truth of the musical expression from all rhythmical fetters, the other, the accompanying hand, continued to play strictly in time.
A music critic of the Athenaeum was quoted by Frederick Niecks (biographer of Chopin Frederic Chopin as a Man and Musician pub:1902 It can be downloaded for free at
https://manybooks.net/titles/niecksfretext04fkchc10.html ) as saying
"He makes free use of tempo rubato: leaning about within the bars more than any player we recollect, but still subject to a presiding measure such as presently habituates the ear to the liberties taken."
However Chopin did not tolerate any rhythmical sloppiness, Madame Streicher assures us that he detested any sign of languor, dragging of the time, misplaced rubato and exaggerated ritardando.
And Chopin was a very shy person, not bold brave, not a showman at all.
Chopin to Liszt
"The crowd embarrasses me. I feel stifled by their breathing, paralysed by their curious glances, mute before their strange faces. But as for you, you are intended for them by fate, for if you cannot win your public, you have the power to stun them."
Chopins playing was very delicate, often his p sounds where too soft for people to hear and he would be always criticised for playing too softly.