For this little money, why bother with the warranty?

The horn on my Honda died recently. The car was still very much under warranty - it was only 11 months old at the time. But being a car nut, I took the front bumper off myself (done it before to install foglights) and took the horn out to check it. Yep - dead. The relay worked, I was getting 12v on the power line, but the horn was done for. So I went down to my dealer and ordered a new one - $15. Then the question - 'is this a warranty replacement?'
Well - yes - I suppose so. But it's only $15 and I can do the work myself. Nevertheless, we had to go through the service department to find whether or not I could have the part for free - covered under my factory warranty.
I'm in two minds about this. It seems to be more time and money than it's worth to get Honda to warranty-replace a $15 horn, especially when I can do the work myself. But on the flip side, I'm impressed that they were willing to even talk about warranty replacements given that I'd taken the old one out in the first place.
In the end, I refused and just paid for it myself. I didn't see the point in making Honda spend labour and administration costs to document and replace something so cheap.
I can understand how a lot of people would simply say "But it's nearly new! Let them do the work." But I'm not like that. For the hassle of taking the car in, getting them to diagnose the problem, order the spare, then get the car in again to fit it - that's an hour each time, plus travel to the dealer and back, shipping, labour and administration charges for them. ie. the better part of 4 hours of my time wasted, and probably $300 in labour and associated costs to replace a $15 part.
No - I'll save warranty work for when it's needed - big ticket items.