Reason for marginal revenue is less than price in monopoly I understand the fact that marginal revenue is less than price because in the monopoly firm faces a downward sloping demand curve.

As well as, by expanding output firm is going to lower the all the cost of its previous outputs as well.

However, I don't fully get the picture how this is appropriate.

Is there any good example in real life?
Most internet providers rarely consider to decrease their price to win market shares. One possible reason could be because the additional revenue P(Y) from a new costumer joining the provider, would not compensate for the total loss of revenue P'(Y)Y from the group of regular subscribers (Y = several millions?). Instead, most providers invest a lot of effort to discriminate between these two groups and try to propose interesting prices only for new subscribers.
In "real life", you may not observe such a foolish thing, and will find only few concrete examples of monopolies having reduced their price in the hope of winning market shares. It is not because you do not observe such a behavior, that monopoly theory is useless. Quite the contrary, the chapter explains why you rarely observe such a foolish behavior.