In the medium run (first 2-5 years) it’s not cheaper.
In the short run? Buying Linode gave them a foothold in the market. Creating it from scratch, would have taken months (or even years) to be able to make the first offer, and years until they built a reputation that would attract customers.
But the whole point is that they're throwing away any of Linode's existing reputation in favor of banking on the Akamai name.
Yeah, but that's the big if, isn't it? Once they enact changes which require action on your part (sunsetting services, changing prices, ...), you'll probably move, or at least seriously consider it.
* already existing SOPs and MOPs. Way easier to integrate or copy something that works than building it from scratch
* already existing systems -- ordering gear is still weeks or months out for us, plus no need to engineer or setup a new system as above, way easier to integrate or copy than starting from zero (in a business sense, anyway)
* lingering brand name recognition