According to a book about the Beatles, which I read 25+ years ago, Paul deliberately screamed himself hoarse *before actually recording those vocals in order to get just the sound he wanted.
And I would also like to point out that Geddy Lee stopped singing like that two decades ago.
I think I get what the OP is talking about. If you listen to Ball and Chain, for instance (one of the best damned songs ever, IMO), some of Joplin’s high notes become harsh, gutteral yowls. To me, this adds to her interpretation of the song, and seems to be a trademark for her.
ETA: AskNott said it better.
“Bluesy”?
I so hear that in the voice of Chris Colfer.
Just one more chapter in the history of white popstars trying to sound black. 
Two concepts are being conflated: technique and sincerity/delivery
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Technique: yeah, it’s a bluesy wail. It emerged from the raw, untrained approach that various styles - Delta blues, soul, some country, etc. - have in their vocals. Although it sounds raw, it is often a combination of the singer’s natural tone - Rod Stewart has a natural rasp - and specific vocal techniques. A singer taking that approach without applying some technique over time destroys their voice.
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Delivery: so, what’s the big difference between Lennon on Twist and Shoutand Michael Bolton in When a Man Loves a Woman? Your belief in the singer, in part indicated by how they use that technique. Lennon sounds shred-tastic because he punches his voice - employing that technique after being sick all day, abusing his voice by recording all day, and drinking milk - at all the right spots in the song, and sounds like he means it. Bolton sounds like a douchebag because his technique is there for show, on top of the lyric and not inside it.
Your frustration with this technique is no different than a lot of folks’ frustration with melisma - stretching out syllables up and down vocal runs. In the hands of Mariah Carey, it is gymnastic, syrupy indulgence; in the hands of Aretha Franklin, there are few things as powerful.
I’m going to go out on a limb and say the patina of hipness on Tom Waits’ music supersedes any misgivings the OP has concerning the fact that, in fact, he does practice the same style of singing that was decried in the OP.
I could be wrong, though.
See? I was right after all.
I don’t know of any official name for it. I used to refer to this kind of music as “grunt, sweat & strut”.
There’s a similar dynamic of strain in many bluegrass vocals, in which it’s not necessarily the specific tone achieved which is significant but the “moral” quality of the struggle to reach it, or even the suffering conveyed by the raggedness of the attempt.
The voice is an instrument. You can play it how you like, just like the myriad sounds you can get out of an electric guitar.
I like Janis, Joe Cocker, and Waits. Great vocals!
^^^Agreed.
It’s not just rock and blues. The very worst of these, IMHO who I really can’t stand to listen to, and whose success continues to baffle me, is Garth Brooks.
No, that’s Yoko Ono.
Of course, if you shred the strings on your guitar, you don’t have to have 5 follow-up surgeries to remove the polyps from your fingers…