What is the ruling on the statement that one either maintains all prayers, or abandons them all, and that it is of no benefit to pray some prayers and abandon others, or to pray sometimes and abandon prayer sometimes?

Praying some obligatory prayers and neglecting others is not equivalent to abandoning prayer entirely. The former is doing some good, unlike the latter. The first type is safe from excommunication according to some scholars who excommunicate those who abandon prayer entirely. Whoever prays sometimes and neglects sometimes is subject to the threat of Allah's will, and his obligatory prayers might be completed for him by his supererogatory prayers.