ONE: Pedaling generally has less to do with sustaining pitches or creating legato and more to do with tone color. A note played with pedal has a warmer, richer sound than one played without.
TWO: @ttw makes a critical point that Chopin's piano had less power that a modern piano. It did not produce as loud a sound, and the sound decayed more quickly. Also, the key depth, and even the length and width of the keys, were less on Chopin's piano than the modern instrument. This, too, has an impact on both the power, the tone, and the "legato-ness".
The pedal markings in the first sample posted in the question, I interpret in this way:
- m. 5: the first indication, below the low A, is Chopin letting us know he wants that low pitch sustained until the harmony change on beat four.1 This is best accomplished by half-pedaling through the next two beats.
- m. 6: there is no pedal indicated, because there's no particular pitch that Chopin needs to indicate as sustaining.
- m. 7: this measure is essentially a repeat of the first, and again Chopin want the performer to allow the low A to continue as long as manageable until the harmonic shift.
However, none of this precludes pedaling, or not, wherever the performer feels the need. This Etude begs to be played all out, which on a modern piano means reinforcing the tone as much as possible with the pedal. But the right hand (or left hand, as in the second example in the question) will get muddy very quickly if the pedal is held down, so at minimum, pedaling every beat is a necessity. The technique to apply is sometimes called "flutter" pedaling.
On the other hand, the opening measures can be very effective with no pedal, creating a "dry" sound before the onslaught.
“The more I play, the more I am convinced the pedal is the soul of the pianoforte!”
1 This begs the question of why Chopin didn't write a dotted half-note. I believe that, first, the low A is still part of the left hand "melody", not a separate voice. Second, Chopin doesn't want the sound literally held for three beats. He's allowing for natural decay, he just wants to make clear that the sound has to be gone by beat 4.