Often when I hear "Turing machine," my mind's eye pictures a quaint infinite ticker-tape with a small little machine writing and erasing $0$'s and $1$'s.
But when I'm forced to think about a Turing machine as a tuple of states, blank symbols, alphabet symbols, transition functions, etc., my mind often glosses over.
I live in the 21st century; thinking about computation is so second-nature to me now that I struggle with keeping my mind on such a pleasantly old-fashioned infinite ticker tape. I know pretty well how the computer on which I'm writing this operates, clearly not at the details of the machine code but at a level of abstraction that I feel comfortable with. I also never liked how the alphabet has, basically, three symbols $(0,1,blank)$. Why do we even need the $blank$?
Turing's work in the 30's was baller of course, and there are some well-deserved accolades when the new "smallest universal Turing machine" or "largest Busy-Beaver" are announced. People also have a game of writing esoteric programming languages based on small Turing machines.
But is there a good reason to use the ticker-tape Turing machine for a model of computation, now, in the 21st century? Are there reasons for the formalism still being "worth it?" Or can we just say a Universal Turing Machine as in a smart-phone?
Of course Hamilton's etchings on Broom Bridge marked a turning point in the history of mathematics, but I've read that quaternions per se were oversold by the end of the 19th century.