Is it worth of replacing central AC coil?

It's hard to say but at 16 years old I'd opt to replace the entire unit. My guess is that IF you can find someone to replace the leaking parts, the bill is going to approach the total replacement cost.

But you could contact a couple of local HVAC contractors and get estimates for both options.

Ok if you know 100% it is the coil that is an easy repair. The refrigerant first needs to be recovered the old coil cut out and the new one installed. Coil cost 2 ton R22 ~300$ Plus recovery time and pumping the system down once the new coil is installed. Measure the amount of R22 returned to the system and add the difference for your ~4 lb total . The repair cost would be 1 days work the coil and a couple lbs of r22. Dang the 8k and 10k prices sound crazy to me it is only a 1 day job ok possibly a day and a half if access to the air handler is not so good. But I know R22 is going for 100 per pound 2 lbs plus a coil 500$ in materials ok a a little for the silver solder and flux but other than that the tech time maybe 100 /hr or so it depends, you might get a guy that needs the extra day of work and gives you a onetime good deal. But those are ball park numbers you could work with so you have an idea.