Your laser controller already does this. The reason it’s not cutting through is that it correspondingly lowers the power as well, so you get an even, consistent burn. The 0.9.21 release adds the option to choose ‘Constant Power’ mode for GRBL devices, meaning you can tell the system not to adjust the power based on speed, which is preferable when cutting.
LightBurn already does this. What operating system are you using?