In 'The Mythical Man Month' (which you have read, haven't you?), Brooks says words to the effect that 'conceptual integrity of the architecture is the most important thing'. That means that if the requested feature breaks the conceptual integrity of the overall design of your product, you probably should continue to avoid implementing it, regardless of how much it is requested. Or, you need to reshape the architecture so that the requested feature fits into the revised architecture.
One of the products I work on has a 'much requested feature' that was added. It behaves unlike any other feature in the product. It is a horrid wart. But since the competition does it, we had to do it. But instead of remaining true our architecture (which happens to differ fundamentally from the competition's in this area), we aped the competition's feature, down to silly details.
I still bitterly resent the fact that the feature was botched into the system with broken semantics w.r.t the rest of the product. To rub salt into the wound, I had to present the new feature as the 'greatest thing since sliced bread' to our customer base -- that really hurt.
Having said that, no-one has complained (as I think they should) about the feature. It probably gets used sometimes. It is one less difference that the competition can use against us.
(And note: I was not against the feature being implemented in a style consistent with our product's normal way of working; I was only against it being implemented in the style that our competition uses - because the other related features work analogously to the broken implementation in their system, whereas our system is more sane and friendly.)
It's tough. Sometimes the market wins out.