That theorem just indicates that Turing Machines with an unbounded/arbitrary number of symbols is a poor model; the approach there will not work on any actual machine. If you take out a factor of 2 in an algorithm, that's going to asymptotically double the state regardless of what actual machine you're on, so I don't buy machine-independence as a reasonable excuse. The actual reason constants are ignored is because it makes the math a lot simpler when you ignore them.