I don't know if it's because of another mod but I found dragon eggs in chests while looting an abandoned mineshaft. It seemed that there was an egg in every other chest and it became a concern. I don't want dragon eggs to be a common drop because that just decreases their worth, and I also don't want everybody to have a dragon at the beginning of the game.

The only world-gen/structure-gen mod I have that may be causing these unwanted dragon egg loot drops in chests is Biomes O' Plenty. Hopefully this info may help you solve this issue.

Some other things:
If dragons can breath fire in this mod... I might be stupid for asking but idk the controls for that. I tried pressing R key like in the original mod but nothing happens.

I also noticed there is no config file. This might help for regulating chest spawns.

Dragon eggs can be found in a variety of loot chests. From my initial testing, I have not been able to replicate how common they are like you are experiencing. I will run some further tests and get back to you soon. (I apologize for the delay, as I am undergoing school currently)

the original dragon mounts always had eggs spawning in chests that are in dungeons/mineshafts but i believe they were rarer to find then they are now

eggs dont seem to be inside village or pillager outpost chests from what ive seen but i found a mob spawner that had 2 ender eggs and a water egg in the chests and i also found another ender egg and a couple of fire eggs in a few end dungeon/fortress chest so i think the spawning is a little broken i also know that the eggs just dont spawn in villages or pillager outposts and like to spawn in underground dungeons/mineshafts/spawners if this is any help at all

I'll experiment and try it without using Biomes O' Plenty and see if that's what is causing the problem.

UPDATE:
I finished generating multiple worlds without certain mods, and completely without mods.
Unfortunately the problem still continued to occur, so I assume it has nothing to do with other mods generating structures with chests/custom loot pools.

How I experimented:

1. Removed all mods except the Dragon Mount mod

2. Created a stock vanilla world

3. Teleported all "minecarts with chest" to myself: /tp @ e[type=minecraft:chest_minecart] playername

4. Searched each chest for dragon eggs

RESULT:
Dragon eggs still continued to spawn in "chests" although specifically in "minecarts with chests". I still don't know if it is only within the minecart entity chests or not. I did not take the time to find villages each new world and search in regular chests to see if the problem occurred in both types of chests, but I hope this information is helpful.

I'll experiment and try it without using Biomes O' Plenty and see if that's what is causing the problem.