a creature reads ready fight with a friendly creature. What is the use of this mechanic?

There are several ways to utilize it. I most commonly used it in House Brobnar, where I would play a creature with a fight ability (like Fight: Gain 1 aember), then play a creature next to that one that enabled it to immediately ready and fight. In those instances I essentially got to use the creature's fight ability a turn earlier than usual, thus getting an aember out of using the creature instead of giving my opponent a turn to kill it before I could utilize that ability. Plus the old ready a Brobnar creature, the opponent has no creatures on the board so the card is resolved, then that Brobnar creature could reap and generate an aember that way. Unless it's a creature that could only be used to fight, but I digress.

Hope that makes sense.

I remember when KeyForge was first announced and I saw the line "Ready and fight with a friendly creature", I thought it meant that the creature with that ability would fight another one of my creatures. Coming from Magic: The Gathering and seeing that this was a game designed by Richard Garfield, I was ready to look for those corner cases where this would be useful. But then the actual rules came out and saw that it meant you pick one of your creatures (the friendly part) and you use it to fight.

Where this is useful is if you have a creature that is not your current house, but you play a card from the current house that says "Ready and fight with a friendly creature" or "Ready and fight with a neighboring creature", then you can use those cards not in your current house.

Example: The previous turn I named Logos and played Quixo the "Adventurer" and maybe a couple other Logos cards. After drawing my cards for the turn, I see there is an Anger action, a Ganger Chieftain creature, and aGauntlet of Command artifact. I really want to get the Gauntlet out, but that means I wouldn't be able to use my Logos cards. BUT!!! I can use the Anger on Quixo to ready and fight. It should already be ready from the end of my previous turn, so I do as much as I can and I use Quixo to fight. He has skirmish, so he doesn't take any damage from the combat and I get to draw a card from his fight ability resolving. I can then play my Ganger Chieftain next to Quixo (if there is a space) and his play ability lets me ready and fight with Quixo, which will get me another fight trigger and a card. I play the Gauntlet afterwards, but since it enters exhausted I can't use it this turn, but in future turns where I call House Brobnar, I can use the Gauntlet to ready and fight with Quixo should I want to even though it is a Logos creature.

One of the biggest things you can learn in this game is what cards let you "break the rules". Being able to use cards out of house is one of the biggest forms of card advantage since you are breaking the main rule of the game.