Three-way linking has its pros and cons. After Google strengthened their policies regarding spam, many used methods like reciprocal links have become obsolete and a possible door for penalties. The three-way links logically stepped in the scene.
On the plus side, this is really a safer choice when it comes to your link building. Still, you have to follow the guidelines and only use this method inside a relevant network of websites, so the links you receive are still useful for your visitors. Further more, having the different websites on different servers increases the geodiversity you get in your network.
On the other hand, collecting links without relevance, just to get the numbers up, will still be suspicious for Google and even though the links are not reciprocal you still risk being penalized. Not to mention that if the links does not reflect your business, your visitors would soon be confused and lose interest in your site. Even if you dedicate a whole page for your links, there is still a chance that Google would not like that, simply because you have a whole page dedicated only to outbound links, nothing else.
All in all I get why this is a preferred tactic by many when they build their network of links and like many other things in life (and business) - if you do it right, then you will find it beneficial
