In Melbourne, all VCE (which is Year 11 and 12) mathematics is split into three main outcomes: Outcome 1 is Knowledge and Skills (so all the routine tasks), Outcome 2 is Analysis (so all the non-routine tasks, where you need to get TO the maths before actually doing any), and Outcome 3 is Technology Use. Most schools also follow this format to an extent in earlier years as well. All students are required a CAS calculator. There are always two final exams.
Exam 1 is all short answer, is technology free, and is without notes. It is entirely to assess Knowledge and Skills. All working out is expected to be shown, but a sophisticated result is usually not required (i.e. answers don't need to be fully simplified as there's no calculator, etc). This is obviously to assess that a student CAN do the routine tasks that could be skipped over learning if they relied on a calculator too much.
Exam 2 is part multiple choice, and part Analysis. It is technology active (so calculators are allowed), and a bound reference of notes (either of the student's making or a textbook) is allowed to be taken in. In the multiple choice section, all questions are worth one mark, and no working out is required, so this is the part where we really can assess a student's ability to use the calculator to get answers quickly. This is an essential skill in higher mathematics and in their fields, so it's important that we teach it. The analysis section requires students to read and sort through worded problems (some might be quite obscure contexts) to get to the maths and then solve the problems. The actual mathematics to be used is usually not as in depth as what would be in Exam 1, and students are also expected to use their CAS to help them as much as possible there too, because here it's the analysis of the question, not so much the actual doing of the mathematics, which is the most important thing.
Again, most schools follow similar formats in younger years (i.e. having a technology free and a technology active section in the exams, splitting up into Multiple Choice, Short Answer, and Analysis) to prepare them for VCE.
The structure for VCE maths I feel is the best it could possibly be, as it attempts to build skills, knowledge and understanding, and to prepare students well for how they will be expected to work in their respective fields.
So to answer your question, at least in my area of the world, students ARE allowed to use their calculators, but they are expected to use them as their partners and extensions of themselves, so that they can build their analysis skills and not focus too much on skill and drill.
