Stock HTC got bricked by the latest OTA (4.20) The latest OTA on Rogers (4.20.631) rendered my phone unable to boot and stuck on the white Htc One screen.

I'm on stock recovery exactly to install OTAs, which worked with the last one (4.19?), but not this time.

Here's the logcat when booting up, the part that keeps looping. I can't find good keywords to Google.

Since I am with Rogers (631), there are no RUUs, and I'm reticent to wipe out all my data.
The problem your device is having is that it can't protect an area of memory. This causes ART (the Android Run Time, the system that runs regular Android apps) to crash, rendering your device unbootable.

If you haven't modified your ROM before the update (for example by rooting it, or installing a custom kernel), this was probably a bad update from HTC or the updating process failed somehow. 

If it's not possible to downgrade to your previous ROM, you could try to reset all data. If this doesn't work or you don't want to do that, you should contact the store you bought your phone in or contact HTC support. They might be able to put a working software version on your phone. This might wipe your data anyway though.

If you really don't want to wipe any data, you might be able to "dirty flash" a custom ROM over the stock ROM. This replaces the system partition so that if the system was corrupted by the OTA, it would be bootable again using the custom ROM. The custom ROM has to be the same Android version to not require a complete wipe, and installing it requires you to install a custom recovery. This might also void your warranty.