Orlando's afternoon thunderstorms and the occasional palm frond drop wreck pool cage screen panels constantly. The screen itself is straightforward DIY: $80 in spline tools, $30 per panel of fiberglass mesh, an hour per panel.
Where it stops being DIY: anything involving the aluminum frame. Bent extrusions, loose super-screws into the lanai pad, and cracked corner brackets all need a pro. Frame work involves working at height with rivet tools and proper anchoring into existing concrete.
Cost to fully rescreen a 12x24 pool cage with a pro: $850–$1,400, single-day job. DIY same scope: $250–$400 over a long weekend.
If your cage is over 15 years old, get a pro to inspect the structural frame BEFORE you invest in new screens. Replacing screens on a failing frame is wasted money.