Both of those reasons for using a secondary aren't correct. You may certainly use a clearing vessel (it's not really a "secondary", it's a bright tank or a clearing tank) if you wish but there is no reason to worry about getting off flavors from the yeast. Also, nothing magical happens from moving the beer to make it clear faster- gravity clears the beer and not the act of moving it. It'll clear just as fast in one container as another.
In a brewery, there are a couple of vessels. The fermenter is where fermentation takes place, and then the finished beer is moved to the bright tank. The reason that happens is so another batch can be started in the fermenter, not because the beer will clear any faster in a different vessel.
It's true that you can get off-flavors from leaving the beer on the yeast cake too long- but that's many weeks or even months and not 10-14 days like most homebrewers typically do. Many homebrewers routinely leave their beer in the fermenter for a month with good results. I'm one to package the beer when it's been finished for a week or so and is clear, which is usually around day 10-14 for most beers. For lagers, I do use a carboy for the lagering period and remove the beer off of the yeast, though.
If I use a secondary at all (like for oaking or lagering), I would never use a 6.5 gallon carboy. The reason is that once fermentation is over, the co2 production ends as well. In the original vessel, the co2 that was produced during fermentation but still trapped by the airlock helps protect the beer from oxidation. But once fermentation is over, and the beer is moved, that 1.5 gallons of headspace is a risk since no new c02 is being produced to help mitigate that. If you feel that you must use a clearing vessel, make sure it's the proper size for a batch.