This added to the film's overarching theme of John McClane having the deck stacked against him in every way imaginable.
The theme of Die Hard is that the protagonist prevails when virtually everything is going wrong for him. He shows up under-dressed to a party, makes a bad impression, botches his reunion with his wife, gets caught without even a pair of shoes on with nothing but his side arm against a group of 15 or 20 terrorists with automatic weapons. He manages to kill one and get his weapon... only to find that he just killed the brother of the most dangerous terrorist who is now out for blood (and also that his shoes are too small for John to wear).
One of the main threads of this theme is that the authorities – who should be there to support him – are not only unhelpful, they actually work counter to his effectively dealing with the terrorists. First we have Powell, who initially is going to leave the scene as a false alarm. Then we have the grossly incompetent LAPD commander and his SWAT commander, whom John has to save from their own bungling. Finally, the FBI arrives as the ultimate authority hurdle for John to have to deal with. First they play directly into the terrorists' hands by shutting off the power, then they nearly kill him with their gunships. The LAPD's unhelpfulness is born of incompetence, the FBI's is born of hubris and callousness.
The movie revels in John persistently hanging in there and prevailing against greater and greater (and more and more ludicrous) challenges from not just the terrorists, but from virtually everyone, including the hostages to a certain extent. Only John's wife and Officer Powell are actually competent and helpful, though they are mainly sidelined by other forces through most of it. The cartoonishly arrogant and cold blooded FBI agents are just one more part of this absurd puzzle. Like the "incompetent police," the "cocky and gun-happy FBI" is an old trope – one that dates back to the days of Prohibition when they had to go up against very well armed criminal organizations. It really isn't a fair trope, but it is one that is easy to fall back on when you need FBI agents to be a problem rather than a solution.