I'm not totally in disagreement with you (and the fact is also that I tend to be "hard" when it comes to evaluating things as you do). I also drew a much harder line when younger, and thought emotional appeals were stupid and pointless. Over the years I've learned to make some allowance for them, now that I'm aware of the ambiguities in life, my own limited prescience, and how different people interpret the world.
There is an irritating prejudice against emotions when there needn't be. The origin of an idea does not determine its truth or falsity, and so that an idea has come about from a feeling or emotion should not be important. The idea can then be tested, and perhaps found to be in error, but its falsity would not be inevitable. Therefore, if we turn our backs on an idea because of its source, rather than because we think it is false, then we might also pass by the truth without giving it a fair chance to convince us.
There was a book on self-defence which I once read called
The Gift of Fear. The author encouraged people to trust their instincts (or gut feelings) of danger, and lamented that people would ignore these warnings because they were mere feelings, and instead turned to reason. The issue was not the inability of reason to arrive at the correct conclusion, but its slow and reflective character, which could waste valuable moments when a quick response is needed. Indeed, it seems to me that some people are better trusting emotion rather than their reason, since the former is quicker and more accurate than the latter.
This kind of analysis of emotion can bring to light something which is rarely understood. In short, emotions interpret circumstances and provide the motivation to preserve or alter those circumstances. However, this means that emotions are unarticulated theories, which interpret circumstances theoretically, inferring causes and predicting consequences, and the motivation for action is appropriate supposing that the interpretation is correct. That is what the author of the self-help book implicitly understood. Therefore, though emotion can lead us astray, so can our reasoning if it is poor, and neither has a monopoly on rationality.