Generally lower temps cause a cleaner tasting product. But you'd want the temp to be not too cool either, as too cool will slow it down too much, for no benefit. There is a sweet spot that allows the beer to finish clean and in a reasonable amount of time. Yeast are creatures, and their behaviour is directly affected by their environment, which temperature is a part of.
What I try to do is ferment at the lower end of the yeast's recommended temps, depending on the yeast strain. Let it ferment for 7-10 days, then allow it to warm up a bit for 3-5 days before racking to keg. If I'm bottling it, the schedule might take a bit longer, as I want to let the beer clear a little more. And of course it all turns on my own personal schedule. The 2-3 week timeframe might easily become 4-5 weeks if I'm busy doing other things, or if the beer is stronger than average. (And of course, some yeasts and styles require more time too.)
Lastly, 65-68 isn't that low for most ale yeast. It's about right for some strains, like Nottingham, which tend to throw more esters at 70.