IMO 9 is the fault of the language rather than the programmer. Julia solves this one by having types that can represent conjugates, transposes, and adjoints of arbitrary matrices lazily.
If someone is writing a higher level object-oriented linear algebra environment, having the matrices carry around a "transposed" flag that they can pass to BLAS seems like a reasonable thing to do. Since, other than in Julia and Matlab, matrix stuff is usually an add-on, we can't really blame the language for this decision IMO.
A downside could be -- usually your underlying tuned library will be BLAS and LAPACK, which don't accept a 'transposed' flag for every single operation. So, from the user point of view, it could be kind of confusing -- "when I transpose a matrix and then go on to multiply, the transpose is free. But if I transpose a matrix and then go on to hit it with QR, it for some reason incurs this weird extra cost -- not where I do the operation, but later, in the QR."