Everything you cited exists also in the traditional university system. Projects (one or two per subject per semester, sometime with a high degree of liberty for the details), getting help from other students (just go in the CS student association and ask), tutoring others (I did it a few time), independence & responsability (going only in class you need, skipping others and taking the exams), going beyond what asked (for instance, majoring in two diploma at the same time), etc. You can make your university journey almost anything you want. But the main failure point of most student imo is that they consider the teacher are against them. Some are, but most aren't and are really likely to help any motivated student who ask for it.
So, I thing that the no teacher style school is very bad in the sense that it have no-one to force student learning stuff they don't want to but that are important. This can form bubbles of knowledge with important or interesting things not included. One the reverse, the traditional university still consider students as children (which most are, actually) and does not give enough space to do thing in one's way. It is still possible to go, but it require a lot of efforts.