I guess a HRM is slightly more accurate than perceived effort. A HRM is not perfect, because your heart rate tells you only how fast your heart is beating, not how hard your (other) muscles are working. Taking lactace samples or measuring the Watt output is more accurate, but more expensive and/or more hassle and/or invasive. HRM monitoring is easier/cheaper than these more accurate methods, and still fairly accurate.
I also think that the very use of a HRM with 'target training zones' encourages you to train in a variety of training zones - aerobic, close to threshold, heavily anaerobic etc. etc, and so even if the HRM doesn't give the best in accuracy, you'll probably end up with a training regime with enough diversity to improve a bit on all these counts.
That said, I think my body is reasonably OK telling me when I'm putting in too much effort. I also think that perceived effort and a good sense of target pace / power output have a slight edge over HRM when the time of each repeat during an interval workout is short.
Finally, the best use of an HRM against overtraining may lie in using it for monitoring your resting heart rate. Take your RHR in the morning while you're still in bed, before getting up, and if it's higher than normal, you've got an indication that you may be overtraining, that your body is trying to fight a new ailment or a bug, or that you had too much lemonade the night before :-)