The insulation on my AC pipes looks cracked and soggy, is re-insulating actually worth it and what does it cost in Dubai?

This is genuinely worth doing, not cosmetic. When the insulation on the cold refrigerant line perishes, cracks or gets soggy, the pipe sweats heavily in Dubai's humidity: that means you lose cooling into the ceiling void instead of into the room (so the system works harder and your DEWA creeps up), the pipe drips, and that constant condensation stains and damages ceilings, walls and anything below it. The dampness you are already seeing is exactly that. Re-insulating is a straightforward job: strip the perished foam lagging back, and re-insulate the lines with the correct thickness of closed-cell insulation and a proper vapour seal so moisture cannot get back to the pipe surface. What drives the cost is mostly the length of the pipe run and how accessible it is (exposed runs are quick, boxed-in or high runs take longer), not any expensive materials, so it is usually a modest job with a real payback in efficiency and in avoiding condensation damage. Getting proper AC pipe insulation done, rather than patching the cracked foam, is what stops both the wasted cooling and the dripping. On what you describe, with it already soggy and damp, I would not leave it.