Is it worth taking your dogs to the mine?

In real life.

Fun in Minecraft

Is it strategically cheaper or are you just hurting yourself?

Unnecessary

What are they supposed to do in the mine? Fight the monsters? You can do that yourself.

They bring you nothing downstairs and only run into creeper or lava basins

Cats are more worthwhile because the creeper drive them away. The dogs only monsters, you can kill them yourself.

I would generally leave animals on the upper world.

Otherwise you run the risk of your animal falling into the lava, for example.

Have fun!

OK.

But they do the Usain Bolt Move when I want to tame them😂

No problem I like to help.

Trying to sneak, they don't run

Sneak up to them with fish in hand