I've done triples in conjunction with run commuting. Easy to work, intervals at lunch, super easy home.
I've also done triples when camping. That's more about just getting into a different rhythm. Sitting by a mountain lake, reading and drinking coffee. I just end up running a lot because I feel like it.
I suppose one possible reason to do it would be to influence your hormonal profile and to facilitate better refueling. Running releases growth hormone, so running more frequently potentially means a larger percentage of your day is spent with elevated GH levels. You are also more easily able to replace muscle glycogen immediately after exercise, so doing at least a short run before every meal could help with that.
Anyway, in my limited experience, triples are neither a recipe for disaster nor a secret to success. It's pretty similar to doubles, but less convenient.
Doubles vs. singles, on the other hand, is probably the single most important change most runners could make to improve.