The main advantage of a chemical laser is that you get the energy you need to excite the lasing atom from the chemical reaction, rather having to have a large external electrical source. When you start to look at megawatt laser systems this translates into having a lighter system. Although that may be changing with new generations of fiber lasers and fiber amplifiers.
A problem with chemical lasers is that the chemicals are very reactive, also you deplete you excited atoms as you are lasing so you want to introduce new excited materials into the cavity very quickly. For example from a SPIE paper
You can see that there is a lot going on from handing the reactive, toxic gasses to "scrubbing" them so they don't exhaust and poison people. Scaling this down so it can be carried by a person is not very feasible, since the power output would also go down, and you really need a lot of power if you want to punch or burn holes into things.
Doing this on a truck scale, or on an airplane is slightly more feasible, but such systems are probably relatively fragile and complex.
The next problem if you can produce the laser light at a wavelength that can go through the atmosphere, is that you need to steer the beam and keep it on target, and that the laser beam diverges the farther away you are on the target, so less energy is available to be on the target. To keep the beam small and "divergence limited" you want to have large optics or mirrors. 580
These can be hard to make for high powers, and if they are large it can be difficult to move them smoothly and rapidly.
You can see the size of the Tactical High Energy Laser optics and gimble. You can see it also has to have some additional optics to track the target. This type of system used a chemical laser and demonstrated it could hit drones.
Finally how much can you skimp on power? As the beam goes through the atmosphere assuming you can hit the target, you really do need a lot of energy, and it depends a lot on wavelength, pulse duration, and the total amount of material needed to be removed. The turbulence in the atmosphere will also distort the beam and make the power arriving on the spot variable. Also the type of damage you want to have, heating and burning vs vaporizing matters, but generally these types of lasers are essentially heating up the target rather than vaporizing them. So to have that occur relatively quickly you really need to have hundreds of kW. 580