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The article is full of technical misconceptions, but if I had to guess:

1) Botnets give you a ton of bandwidth to run port scans or crawling searches.

2) They also allow you to "map" port scans or searches over thousands of computers (e.g. one computer in the botnet scans one specific port times ten thousand ports), obscuring the fact that a scan is even occurring.

Funny enough that question was answered in a rather public way just a few weeks ago: https://news.ycombinator.com/item?id=5404642 (Researcher sets up illegal 420,000 node botnet for IPv4 Internet map)

I did read this article a few weeks ago but seem to have forgotten its link to my question.

Thank you for the reminder.

I think it's because you can use botnets to divide up the vast IPv4 search space among the individual bots and crawl it exponentially faster.

Exponentially?

If you assume the bots are infecting hosts they scan, then yes.

I think exponentially is the new literally.