It is important to understand here that the no-slip condition is actually a more realistic condition that represents the fluid behavior more accurately. Experimentally, it is known that for all real fluids, the fluid particles with immediate contact with a solid surface, move with the velocity of surface itself. When the wall is stationary, the particles near the boundaries will have zero velocity. According to Newton's law of viscosity, the particles to a depth near the wall, will experience resistance and will observe a decrease in velocity. Further, as stated by Brian, this requires the velocity of particles away from wall to increase to keep the mass flow rate constant.
This is not a limitation on Discovery Live's part and I believe this is the correct representation of a practical application as this establishes the required consistency in mass flow rate. Had the particle velocity not increased, the net mass flow rate would have experienced an unintended drop owing to the reduction of speed of fluid particles near the wall.
I tried a sample case and could see that though the max velocity increases from 10 m/s to ~14. 5 m/s before stabilizing, the inlet and outlet mass flow rate still remains almost constant. It can also be seen from the picture below that the particles close to the wall have velocity < 10m/s and this is compensated by the particles near the center, in order to ensure the inlet mass is equal to the outlet mass, which is must have as per the continuity condition.
A free-slip condition on the other hand (though not exposed in DL), would give a more uniform distribution of velocity and seems to be what you are looking for. I must add, such a distribution is approximate and no-slip condition is always a better representation, closer to practical scenario. The free-slip condition is not exposed in Discovery Live and in case if you are willing to use it for some reason, you may have to opt for Discovery AIM. Below is a snapshot of the flow developed using free-slip condition in Discovery AIM (just for your reference), and it can be seen that the velocity if fairly consistent across the section.
Thanks & Regards,