MacBook Pro 2016, TouchID and FileVault

Has anyone managed to get TouchID and FileVault to work on a MacBook Pro 2016?

I commissioned a new MacBook Pro 2016 to replace my MacBook Pro 2014.

My old machine did not have FileVault enabled and it had automatic login enabled. When I used Migration Assistant to transfer my files to my new machine, I took the opportunity to enable FileVault on the new machine.

I found that on my new machine, I wasn't able to use TouchID because it claimed Automatic Login was enabled. However, when I went to System Settings / Users & Groups / Login Options, Automatic Login was clearly shown as off, and indeed locked off (because FileVault was on).

I eventually realised that I needed to switch FileVault off, to re-enable the Automatic Login switch, then toggle the switch to off. I did that and it worked. I enrolled three fingers into TouchID and all was well.

Until I switched FileVault on again.

Then, I discovered that TouchID had no fingerprints registered for me. Fair enough, I would enrol some new ones. Unfortunately, when I tried to enrol new fingerprints I got the message "Fingerprint limit reached.".

I thought perhaps there were some ghost fingerprints hidden by FileVault that I could exorcise. So I disabled FileVault, re-enrolled my fingerprints and deleted them all, hoping to somehow clear the registry of fingerprints. I then switched FileVault on again.

Still no luck. With FileVault enabled, TouchID reported "Fingerprint limit reached", although no fingerprints were shown registered. So, off with FileVault again.

At present, I have my new Mac (which, in spite of the problem above, I'm enjoying immensely), but I have not found a way of using FileVault and TouchID at the same time.

p.s. This has been a painful process. I have c. 1 TB of data so switching FileVault on or off takes a few hours each way. Moreover, I can't quite believe that sweeping all those files several times won't have left them untouched. I'm currently having to rebuild my mail database and re-index spotlight, having found the index was missing files and mail was missing messages. I hope these last symptoms aren't related.

p.p.s. I have no particular need to encrypt my files with FileVault, I'm only concerned that if I don't enable FileVault, someone else might, and so lock me out of my data.