I believe pokestops, should have a small chance to give a egg. (rare or an event egg during a event.) Also I think that you should vote for the server and once it reaches the full 24 hours after your first voted it will give you the items for voting like 4 hours ago. This will prevent the issue with voting then having to wait another 24 hours if your voted too soon. However there should also be a mechanism that only allows one vote from the page to go through.
Meh honestly I think it is fine if you can only get them from voting as you have 4 chances a day to get one. If they were available via pokestops, you could easily farm them for hours and if rng was on your side... you could easily get a ludicrous amount of eggs in just a few hours. That's not how voting sites work. You vote, you get the reward right then and there. Pro tip: Do /rewards first as this tells you if 24 hours have passed yet. That makes zero sense as you have to be logged in to get your items. Currency is possible if you are offline, however physical items... if you aren't online with an open spot in your inventory, where is it going to go? No where.
You'll never get eggs from pokestops, the staff team has said this in the begging. Secondly pokefind doesn't control voting sites and they work in a particular manner.