If you have two entangled spin-1/2 particles entangled in the Bell state |\phi^{+}> = \frac{1}{\sqrt{2}}(|\uparrow\uparrow>+|\downarrow\downarrow>) (I am assuming here that you are familiar with bra-ket notation), a measurement on one of the particles yields the state of the second particle via the partial inner product.
For example, if the first particle is measured to be in the spin-up state |\psi> = |\uparrow>, then the resulting state of the second particle is given by the partial inner product <\psi|\phi^{+}> = \frac{1}{\sqrt{2}}|\uparrow>.
Ignoring the 1/\sqrt{2} normalization factor, this tells you that the second particle must be in a spin-up state.
It seems to have no practical use so why does the universe enforce this rule, how would reality differ if it wasn't true.
Based on what I have said previously, all entangled states of particles must exhibit this type of behavior - that is, measurement on one of the particles will affect the physical state of the other. What your question appears to be asking is, what would happen if entanglement was not possible in this universe?
In that case, physics would be restricted to separable states. By definition, separable states are all quantum states which are non-entangled. For the case of a single particle, there would be no discernible difference between standard quantum theory and your theory, as entanglement is only possible between multiple quantum objects (such as two particles).
However, for multiple objects things really break down, and we actually do need these entangled states to correctly describe reality.
