in your title you state that this is an issue.
It's really not, actually.
It's a matter of taste, so you should try both and hear how you feel like it.
That said, consider the fact that if you DI it, you'll have more control over the post-production, since it's cleaner than mic recording. If you for example put a delay or reverb on a mic session, you will also delay and reverberate the back ground noise. This is far less of a problem if you use DI.