I thought I once read that, since Touch ID relies on fingerprints, a US court order can compel you to provide those, thus forcing you to unlock an iPhone in question. This, as opposed to a passcode-only configuration, which a court order cannot compel you to give (I believe since this would fall in the category of 'forcing you to testify against yourself'). If that is indeed the case, I imagine it would make better s…
It's not too difficult to swap a home button yourself with the right tools, or most stores will do it for ~$49 to $59 (depending on your iPhone model.)
If you have a store do it, definitely ask for your original home button back in case you change your mind later or sell your phone.