The straight answer to your question is that eliminating the eccentric will speed up the time until you can next do the same exercise, and will reduce soreness. This is what powerlifters do predominantly, and I would have to say that doing eccentric contractions is 'unnatural' in the sense that there would not have been many cases when our ancestors would have attempted to slowly and gently lower that heavy carcass to the ground, or slowly lower that big log onto their chests LOL. This form of training is great for the neurological benefits of more frequent ultra heavy training, allowing you to push heavier 1 rep max's.
However, unless you're taking supraphysiological doses of AAS (or have a mutation in your myostatin gene), catabolism is absolutely necessary for muscle hypertrophy in adults. To remodel a muscle, you must tear it down and build it up again. This is why you will see Olympic level powerlifters who are under 60kg, but can lift a million times their bodywieght (OK I exaggerate a little). They're lean and muscular, but do not have a lot of muscle mass for their strength. In other words some level of microtrauma or catabolism is necessary for optimal muscle growth.
There are many different ways to accomplish this. Frequent training with only small amounts of muscle damage may elicit the same amount of hypertrophy as less frequent, more damaging training. But if you look at the area under the curve for markers of muscle damage and turn-over, you will see they are the same. As I said before, if Hannibal completed the same leg workout as me (weight adjusted for his strength levels) and created the same amount of microtrauma, he would not be able to train his legs to the same intensity the next day, or for a couple of days. Like wise if I trained like Hannibal, once I got used to the training my recovery would be a lot quicker than it currently is, though differences in age and gender mean I will prolly never recover as quickly as him.
Hannibal and I obviously have a difference of opinion, and I don't see it as a black and white issue. However, if you're only interested in mass gains, then make sure you have some eccentric movements in your training, and allow time for recovery. If you're only interested in strength gains, then drop that weight like a hot potato, or stick to concentric-only type moves, and train your heart out every day if you wish. More sensibly for most women, I would say a combo of both is good. This is part of the idea behind changing your workouts regularly. Try frequent concentric training for 6 weeks. Try less frequent training where the eccentric is emphasized for 6 weeks. Try 6 weeks where you mix them up (concentric one week, eccentric the next week)etc...... Be warned that 'emphazising the eccentric' does NOT mean doing nothing but eccentric movements. It merely means adding them into you program, and allowing more recovery time between exercises.
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