I'm in the "no" camp, myself. Reasons are twofold:
1. I'd simply rather spend the time and energy on something of my own. Now, if I hear an existing song, and I like it...I just leave it at that.
2. A remix can never really be your own. It's like fanart or cosplay: You're ultimately (where OCR is concerned) just giving free promotion to what is, at the end of the day, a consumer product.
Regarding that, I remember about five years ago, one of the gecko or frog users said that he found the problem with remixes was that no one actually gave a damn about your original stuff by comparison, and it's haunted me ever since. I suspect most people listening (outside of OCR) are listening more because they like and have nostalgia for that game rather than the composer. It would be an interesting survey to see how many actually even know the composer's name. I also doubt that most, unless they're regular listeners to OCR specifically, have any particular loyalty to any remixer.
Not that I regret anything, of course, but that's my reasoning.
Yes, I am an old man, and yes — I yell at clouds.