In my particular case the HDMI goes directly into a sound bar which does not have a DP input. I assume most people building a box like this will connect it to a TV, which is most commonly HDMI-only. So technically not a strong requirement but practically almost

My monitor doesn't have a DisplayPort port.

Not sure why you got downvoted for this - all but the cheapest monitors include DisplayPort because DisplayPort is both technically superior to HDMI and royalty-free.

The only thing HDMI really has going for it TV's/home theater equipment. (And that's partially because most of the manufacturers are part of the HDMI forum, so they're the ones receiving the royalties that everyone else pays to use HDMI.)