Google is, and had always been, a leader in emerging technology and they are diversified enough to maintain their market holdings. They cannot afford, nor should they, to become embroiled with each and every development. They need to be discerning and strong enough to support the decisions they make, not second guess themselves at each turn to maintain their leadership role.
No, they should not have pursued this app any more than they did. It was not a very good app to begin with, and they needed to just forget about this one, and go and come up with something a lot better that would have a whole lot less problems.
I personally think that Google should not have been pursued by WhatsApp more diligently because Google already has a lot to offer because they have GooglePlay, shopping, etc. I personally think that Google should not have been pursued by WhatsApp because it would clash as far as apps to offer.
Google was smart in not purchasing Whatsapp because of the extremely high purchase price. Google offered ten billion dollars but Whatsapp turned it down. $19,000,000,000 was way too high a price to pay for the messaging service. The app is growing very fast but it doesn't generate the revenue to justify the price.
The high technology industry is very volatile, and the fortunes of companies can change very quickly. Although WhatsApp rose very quickly, it could be abandoned by users just as quickly. Facebook will discover in the future that they wasted billions of dollars on a product which is indistinguishable from its rivals.