Coherent = Incoherent

In general coherency of light is discussed in conjunction with interference effects. I will focus on interference effects, because interference effects are what is actually observed.

Astronomers measure the spectrum of a distant star with diffraction gratings. This works because the star is far enough to be in effect a point source.

Conversely, if the light source shining on a diffraction grating is not a point source then there is so much overlap on the display screen that the image is blurred.

The significance of the source being a point source is that that gives rise to consistent differences in pathlength for travel through the respective slits of the diffraction grating. The better that consistency of pathlength difference, the sharper the image.

That consistency is sufficient, as is evidenced by the fact that as soon as high quality diffraction gratings became available astronomers started using them to obtain high quality spectra.

So I think it's a stretch to suppose that light leaves a star as incoherent light and over time behomes coherent. The decisive factor is the point source character of a sufficiently distant source.

Also, I think it's easy to slip into a suppositon that only laser light can give rise to useful interference effects. Counter-example to that: in the Michelson-Morley experiment white light was used. Sodium light source technology was available at the time, but for the setup used white light offered particular advantages.

About light emitted by a laser.

Laser light is highly monochromatic and such a level of consistency of the source alleviates types of restriction on the setup, for obtaining whatever type of interference effect the researcher wants to obtain.

Let's say you have a source of laser light that at any instant of time is highly monochromatic, but there is random fluctuation in the frequency over time. Let's say the setup has some of the light travel a comparatively long distance, and some of the light traveling a much shorter distance. If the fluctuation in frequency is slow enough the light when recombined (to obtain some interference pattern) is still monochromatic with respect to each other, so you still get good consistency.

The slower the rate of change of random fluctuation, the lower the restriction on difference of pathlength

On the other hand, if the light source does not have any temporal coherency (not a laser) then the demands on the accuracy of the setup are very high. Then the pathlengths must be matched to optical accuracy.