How I understood it, and please correct me if i am wrong, is that a machine than can caluclate numbers with infinite precision in constant time has certainly a time benefit, but not necessarily a broader class of computable functions compared to a Turing machine. I interpreted z3phyr’s reference to Wikipedia as a hint to that idea. But I agree that the most convincing arguments are against the existence of such a machine.
(By the way, writing "No.\n\n" can be received as a rude response. I felt a little bit uncomfortable reading it.)
The line of thinking is, "Well, if we had real numbers, we could compute uncomputable functions." No shit. Most real numbers are not computable. If you start with something not computable, you end up with something not computable.
The big problem is that there is no way you will get more than several digits of precision on anything. The next problem is that there's zero evidence that anything in the universe is capable of encoding an arbitrary real number, even within a given bound. The last problem is that making a "real-number" machine capable of solving a problem that a Turing machine can't basically requires knowing the answer ahead of time and encoding it into the real-number machine as a constant. Unclear how you'd do that.