That really isn't true. If you have the CNOT gate, controlled rotation and phase shift, you can implement
any operation on a set of qbits. If you then have quantum registers, you have a truly universal quantum computer, as you can then use registers to chain operation arbitrarily.
This computer would be able to do Shor, Grover, QAOA, as well as any classical algorithm of course. If you're interested, I can try to describe the proof of universality, it's just a bit of linear algebra. Otherwise, you can look up "Solovay-Kitaev theorem".