I agree with the first part about it being Slayer's claim to fame, especially in the wider metal community. Those who deny The superiority of Hell Awaits are obviously objectively wrong, though.
I have a bit of a bias towards Show no Mercy, but I think I can agree that Hell Awaits is Slayer's distinct sound at its compositional best. I wouldnt go so far as being indisputable about it being the best though.
As for the influence on death metal, and extreme metal in general, I don't really agree. I tend to hear more influence from Hell Awaits in most of the extreme metal I listen to than RiB. Especially the the warped song structures and riffing styles from Hell Awaits. Take a massively Slayer influenced band like Morbid Angel for example. I'm pretty sure that going in to Altars of Madness they were listening to far more HA than RiB.
To me RiB was more symbolic of pushing the boundaries of thrash to make things even faster and more extreme, so I think its influence could be seen as more of a change in ethos than simply just a musical influence. As for MA, you can see how they tightened some of the ideas up from the pre-RiB Abominations of Desolation album that eventually appear on Altars of Madness that I cant help but feel was influenced by the more straightforward and aggressive approach on RiB. Considering that they already laid the groundwork for their sound before RiB was even released, id have to concede that it is a primary influence, but the polishing up of their sound for AoM and distancing their sound even further from thrash was definitely RiB influenced. I wont deny the Hell Awaits influence though, which is probably one of the bigger influences in their jam sessions that led to the initially rejected AoD.
For Puppets it even goes beyond thrash; they influenced prog metal bands (Dream Theater, FW circa No Exit, Confessor, etc), they influenced melodeath (the melodic approach in the Puppets bridge or Orion on a whole have definitely been imitated), with that album (and RTL) they really pioneered a more elaborate and BIG songwriting approach that most other bands weren't doing.
Good point. I tend to focus on Metallica's influence as being the catalyst to thrash metal, but what you describe is probably the larger chunk of their actual musical influence.
I guess ill bite. This is based on enjoyment since that is the point of rating these albums:
Paranoid - 6/10 - dont kill me, I just cant stand Iron Man or War Pigs any more. They are anthems for aging bikers who grew up in the 70s as far as im concerned.
Sad Wings of Destiny - 9.5/10 - Not 10/10 because I think Stained Class is stronger.
Reign in Blood - 9.5/10 - I think ive already said enough about this one.
Master of Puppets - 8/10 - Possibly a generous rating for me these days, but my overexposure to this album as a kid was my fault.
Epicus Doomicus Metallicus - 10/10 - I hate giving out perfect scores, but this is about as good as doom gets imo.