> beside of how easy it is to destroy from orbit the anti-satellite missiles coming out from the atmosphere,

No state has deployed a kinetic or explosive weapon from orbit to strike a ballistic missile or launch vehicle during ascent.

No operational system exists where satellites are used as strike platforms against Earth-launched rockets in real time.

Russia has done ground-to-orbit anti-satellite missiles though.

Any directed energy system shooting up would be strictly easier than one pointing down, not only because of thermal issues and power supply but also because it's easier to hide ground installations than satellites.