History is full of timelines and it goes through steps. If a particuler entity didn't exist more than likely that step in history would still happen, just not as quick. When Slayer hit the scence in 1983, there were Extreme bands such as Venom, Metallica, and Judias Priest, but Show No Mercy took it to the next level of extremity. 

In 1985 When Possessed hit the scene, Slayer were the kings of Extreme. When Sepultura put out Morbid Visions, Possessed was the Kings of Extreme.  At this point the Extreme Metal fuse was lit. 

Close to a Hundred Hard Rock , Classic Rock, Blues and Classical artists helped dig the foundation so that Black Sabbath could start building the Heavy Metal mansion in 1968.  If I mention one, that will lead to all of them being mentioned. This controversy is one of the many examples of how an overly opened mind is open to infection. The people I speak of also have created the "who was the first Death Metal band" controvery. Next, we will bring this so-called controvery to an end with facts.  This isn't rocket science, it's Heavy Metal History! 

So to be a part of this discusion, part:1 is to study the different genres of Extreme Metal that came about during the late 70's with Venom (Heavy, Thrash, Black, Punk) and Mercyful Fate (Heavy, Hard, Black, Symphonic) the creators of the early Extreme. Leading up to the 80's explosion of Death/ Thrash, Death/Grind, Prog Death, Melodic Death, Early Slam/Death, Death/ Punk and blast beat driven brutal Death Metal. 

The Building of the second story of the Heavy Metal Mansion, The Early Extreme: The Metal landscape in the late 70s Consisted of Heavy, Hard, Doom, NWOBHM and Power Metal. All of the bands at this time were being attacked by the PMRC and others and being satanic. Venom and Mercyful Fate would proudly serve up some classic satanic Black Metal for the Heavy Metal Masses and change everything. 

The Godfathers of Extreme Heavy Metal Music are Venom. In 1980 they released the first early extreme track known as In League With Satan. In 1981 Mercyful Fate created Symphonic Black Metal. Both of these pioneers mixed in some Black,  Thrash, Heavy, Speed, Power and (in the case of Venom) NWOBHM and Punk into their Heavy Metal drive. Celtic Frost, Bathory, Sodom and about a half dozen more bands helped create the Early Extreme movement. 
1984: Possessed was the first to add (the key word being add) in early forms of Death Metal. If they had a faster drummer they probally would of been a true Death Metal band. The Bottom line is that Possessed created Thrash / Death Metal.   
 

Morbid Angel had the best of both worlds going on in the 1990's. Along with Terrorizer they helped create Blast Beat Driven Death Metal and Grind in the case of Terrorizer. But Morbid Angel just like Death, mixed in some groovy Thrash Metal beats with a Death Metal drive. The biggest difference being the fact that Death was never blast beat driven, and Morbid Angel never mixed in Prog into their drive.  Around the same time you would have Obituary laying down the blueprints for the Slam related Death Thrash rooms in the Heavy Metal Mansion. 

Napalm Death in the 80's was a Hardcore Punk band that when it was all said and done is a one of a kind mixture of Venom and Terrorizer. Hall of famers without a doubt!

Not all Death Metal is blast beat driven. Gore and Slam helps to define this.
Not all Death Metal Bands growl aka Cookie monster Vocals. 
Vocals and Speed don't define the genre. 

This topic here is a opinion piece that includes facts to back it up. The so-called Big 4 is one of the many Metal controvesies. Many believe and I agree that some West coast Thrashers should be included, but not all of the 1980's west coast Thrashes can be on the list.  What about the groundbreaking Thrash Metal hall of famers that came from other parts of the world. Sepultura, Kreator and Overkill are as important to the whole sceme of things as can stand toe to toe with the big 4. 
Groundbreaking moments in time combined with past and current Influence and album sales dictates the majority of this.