Just my opinion:

Tearing muscle fibers and the subsequent healing process is how muscles get bigger, and thus stronger.

Exercising without building muscle mass is nothing more than a cardiovascular workout (increases efficiency of oxygen and nutrient transport, and eliminates wastes built up in fat cells, and also increases weight loss) and only increases endurance, which is by the way, very healthy.

Both kinds of workout burn calories, so if weight loss and endurance is all you are after, I would suggest a full body cardiovascular workout such as swimming (esp. hard-core body surfing), bicycling, and even trail running and hiking without a pack.

Having more endurance is not the same thing as having more strength, although it might seem to be because more pushups can be done. If you don't believe me, lay on your back and lift the heaviest weight you can once and write that down. Now do your 6 weeks of pushups without tearing muscles. You can do many more pushups at the end of six weeks because your body has become a more efficient and cohesive system. Now get on your back again, and I assure you that the amount of weight you can lift will not be significantly increased since your maximum six weeks before.