My view on this is that one should aim for a smooth flowing, legato movement up and down the keyboard, if playing arpeggios as an exercise. It does take practice but can be achieved over time.
I can understand the quote from Chopin - arpeggios appear in music in many different ways and there may be occasions when a smooth legato is not required or not so important. Each situation must be taken on its own merits but for general practice, I would aim for legato, certainly not using staccato to get me from one hand position to another. The wrist does become more flexible with practice.