It is precisely this ability to map seemingly arbitrary and meaningless physical manifestations of turning machines to the abstract that provides the concept so much power. By being able to provably map the implementation to the concept you're able to get all the "benefits" of the concept without having to individually prove them in your implementation where it might be really difficult or just time consuming to prove everything individually.
This, coincidentally, is the same reason mathematics is so obsessed with isomorphisms, homeomorphisms, homomorphisms etc. They are all different ways of saying "this thing stays the same, even when it changes" which many times means that things proven in a place where it's easy to prove are maintained in places where it's very difficult or even impossible to prove (absent the isomorphism).
Transmission, storage with magnetic interactions of electrical actions, small size of components, speed of transmission -- aren't these properties that make for more practical Turing machines?
Parked cars are going to take ages to do anything useful with, no.
(IANAComputerScientist)
No one disputes that a modern computer implementing a Turing machine is going to calculate faster than manually manipulating MTG cards.
However, better here means 'more expressive'. Turing completeness is concerned with whether or not a computational system is 'universal' or not. In other words, whether that computational system can compute everything that another computational system could. If two systems can both be shown to simulate a Turing machine, then that means that those systems could compute the same exact set of things (given enough time).
So with regards to expressiveness (or the things a system could theoretically compute), since a modern computer can implement a Turing machine and a MTG game can implement a Turing machine, they are both the same, and thus neither is 'better'. In other words, the addition of electricity doesn't effect what a system could theoretically compute.