Or is it worth program for higher education in the field of project management to offer to those who already have work experience or a first degree as a specialist?
High school: by all means. Depending on age, I would use "projects" like cooking an exotic dish or baking a fancy cake, starting by procuring (difficult to find) ingredients, ensuring right tools, etc., including suitable evaluation of the final product.
First degree: building a tree house (no experience), cottage of logs or timber (some experience), etc.
In every case milestones and critical paths should be planned ahead and project progress should be suitably documented.
Seconding Lepopld's notion. It depends on what project. Organising a birthday, fine, relocating a business, not fine. Do not underestimate your class but also do not go too far beyond their horizon.
Well, for example - for construction idustry - can we make good project managers in technical university using absolutely unexperienced young students as an 'input material'? Or, may be, more resonable make some input requirements for this specialisation - as a bachelor degree in construction engeneering, work experience in construction (any role), e.t.c.?
a very generic teaching is the best preparation. It should be levelled just above the student's average capability and gradually push their limit further. This is how our MSc approached the topic. Challenging and above your capability but achievable if you widen your horizon and skills (e.g. by researching the task).
Pre-requirements are a double edged sword. On one hand you can specify the PM side of input (e.g. a course in Construction Project Management or Software Development etc). On the other hand is the PM frequently tasked with non development tasks such as scheduling, costing, risk etc. with limited involvement in the actual development/execution. Leaving the execution to task experts has advantages for both sides.
My ideal solution would be a generic BSc in Project Management followed by a more specific MSc in PM with a focus on the specialisation (IT, Construction etc) as well as topics linking Strategy with Projects, PMO, Portfolio Management.
This leaves your MSc(s) open to specialists such as architects, programmers and the like and allows the BSc graduates to continue their education and specialise. Mixing the two crowds would also benefit students learning experience.