Consider a rotating disk on a horizontal plane with static friction. The contact point of the disk with the plane has null instantaneous velocity. Assuming the center of the disk has fixed $v_0$ velocity at a time $t_0$, is it right to conclude that the disk will stop in a time $t_1 > t_0$ by effect of the momentum of friction force? (By the Euler second law we get a negative angular acceleration)
The contact point of the disk with the plane has null instantaneous velocity
This implies that there is no slippage, and as such there are no non-conservative forces doing work on the disk. Assuming the disk is perfectly rigid and is not being subjected to any linear or angular accelerations, the disk will continue to roll forever, and will not come to a rest in a finite amount of time as you are suggesting.
Consider a rotating disk on a horizontal plane with static friction
Note that there is no static friction experienced by a freely rolling disk on a flat plane. If you state that the disk is experiencing static friction, then there must be some sort of force or torque being applied to it.
A rolling disk will eventually come to a stop due to rolling friction. While an ideal disk may not be compressible, and so would avoid the bulk of rolling friction, there must be a contribution from surface adhesion. The molecules of the disk bond with the molecules of the surface when pressed together. As the disk moves forward, it must constantly spend energy to break these bonds and (over a long time perhaps) gradually it will slow to a stop.
To convince yourself of this, consider an ideal disk with duct tape around the rolling surface, sticky side out. It is incompressible, we can assume there is no slippage, and there is a null instantaneous velocity at the contact point. However, there is no doubt in anyone's mind that this disk will not continue rolling forever.
Most materials don't stick like duct tape, but the principles remain. In a finite amount of time, the adhesive forces between the disk and the flat surface will bring the disk to a stop.
A rolling disk will come to a stop eventually because any incidental friction will decellerate the center of mass. Ideally with a flat surface, and constant motion there should be no change as there will be not friction required to keep the disk rolling.
In real life though, for sure a rolling disk will stop eventually.