Taming changes their color, cheese to tame them, and they attack, can kill, and "eat" Cave Spiders, ENDER MITES, And Silver Fish! And they may even be able to attack and kill bats too!
Also able to scout and find cave spider nests, dungeons, ender portal blocks, chests, minecarts, ender mite spawn points, silver fish spawn points, shulkers, ocelots, bats, and emeralds.
They would NOT be too good in a fight against anything else really so fighting bugs would be a good use for them as well as scouting.
And by "eat" it may not do anything unless these types of mobs drop some form of consumable item the Rodent may be able to eat... so for now... it "eating" these other mobs would be in name and animation only... basically it is naturally pre-disposed to attack these creatures automatically in the wild. Tame ones are best suited to combating these mobs specifically as they deal the most damage to them than they would to other creatures including players.
They could ACTUALLY eat seeds, carrots, potatoes, POISONOUS POTATOES (would give a use for those finally), wheat, sugar, pumpkin pie, cake, hay bales (would break into multiple pieces with one missing from a full bale), mushroom soup, cocoa beans, cacti, bones, and flowers.
Wild or tame ones could chew up and be able to destroy (and/or eat) feathers, iron bars, chests, hay bales (would eat one piece of it and the rest would drop as wheat bundles), flint, tools, arrows, bows, anything made of wood or sticks, anything made of iron (except iron ingots), red stone (IRL mice chew through wires all the time), cocoa pods, cacti, flowers, bones, and sponge.
Would be able to dig through dirt, coarse dirt, gravel, and sand... when it digs it destroys the block it is digging in to... if it digs into gravel or sand it destroys the sand or gravel block it digs into and can die if the blocks above fall on it... however if a block does fall on it and it is suffocating it can dig itself out to try and not die.
Rats and mice are EXTREMELY resilient against fall damage and drowning IRL... so it could have an air bubble counter 4 times longer than an unboosted player... and it's suffocation stat would be the same... rats and mice can hold their breath for a VERY long time... so they would need to be able to not die from suffocation unless they get suffocated a BUNCH all in a row... like if it digs up into like... 10 or 20 stacked blocks of sand and gravel back to back and keeps getting hit with suffocation damage... THEN it might actually die.
And fall damage should be like... 9 blocks and it does not take damage... higher than that takes normal damage meter like everything else.
They should also be able to swim at the same speed as a player with Depth Strider Boots, and run as fast as a player running at full speed on flat ground.
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Complete support!!! I understand that they aren't that useful but honestly there are a lot of things that aren't useful in minecraft! Like polar bears, they just walk around and you can't tame them and they only drop fish on a rare occasion. Also the only reason I download mods is so that I can tame more animals and the reason I found this is because I looked up rat mods, but this would be so much better then a mod! I think that maybe they could climb walls like spiders and jump over fences, because as a rat owner I know that they seem to escape everything and maybe even they can pick something up and bring it to you or hold it for you, or they can dig into caves for you (a bit OP but I bet if Mojang did make this happen they would tweak it). Any way I think just how it is right now it would be awesome just like the whole sitting on the shoulder thing. Also one of my rats, Moon, looks like yours! The other is Luna and she is Albino with cream colored splotches, so if that could be one variation it would be so so soooooo coo!! Again I completely support this!
If Mojang doesn't do this then someone should defiantly make this a mod...... I can't I have no idea how to.
One more thing to the people who argue about them being useless, if Mojang actually took this and hopefully would put it into the game then they would fix what they needed to so instead of us arguing over it lets just kindly make suggestions and then the game creators can have the final say! Not trying to be rude or offend anyone!