Tamed Hesperornis WILL lay golden eggs, just takes a bit of time. I had mine on follow in the Redwoods river, and whistle attack targeted it on a fish. It must kill and harvest SEVERAL fish before going on land to lay an egg. It will either lay a normal duck egg, or it will lay the golden egg. It seems to be random, however mine laid about five normal eggs for every golden egg. If the type and size of fish matters, I have not figured that out yet. It will usually kill all types in one shot, and it will not agro every single sabertooth Salmon in the vicinity when it kills one so don't worry about them ganging up on your duck. I was using a lvl 80, probably tamed around level 50 or so and all I put points in was health. Have it kill every single fish in the river before you give up trying for that golden egg. It will happen, give it time. Hope this helps :)
These creatures are great for early players as they are a good source of oil (That I use to make grenades and destroy my enemy) and to get the oils you grab it's egg and throw it in a cooking pot and there you go, go make grenades and ruin your neibours stone base :D
Though most people think of the Kairuku when it comes to Organic Polymer, Hesperornis also drops some, which makes it valuable to early-mid game players who don’t want to risk heading north. As with Pingu, club it when dead to obtain more polymer.
Even though on the wiki it says its a small egg type that makes simple kibble, the regular egg will NOT make kibble. The reason for this is that if you cook the egg without the other ongredients it turns into oil. This mechanic overlaps with the new kibble system and as such, it turns into oil before if can become kibble.
Use them to get primed meat and primed fish. Make sure it is on hunt and retrieve. Put it on you shoulder and aim your crosshair and hit ff while on. Use a axe to get you primed foods once bring back to you.