most air-conds now have. mine dont..hehe

If it's quite bad, then replace it (blower unit). There are many re-con blower out there, as generally parts that spoil are outdoor-compressor and the indoor-control-board. If you get the same exact unit, keep the old one as spare parts (board).

You can imagine, fungus is like moss stuck on rocks. Lightly brushing it only remove the top layer. To remove the bottom layer (remove all), you need to scrub hard and this will obviously damage the fins.

But ... it's in a coil, hence quite impossible to scrub it at all.

Hence, chemical wash using strong acid. It may wash away 80-90% of it... but again, with that strength, it may also corrode the fins. There is no obvious solution to this.

Fungus appear due to water condensation. Before switch off the aircond, my practise is to raise the temperature back to 27-29 C and let it run for 10 minutes. Open the room door and windows to let the air mix around while it is running.
Otherwise, you can imagine, you take out a can of soft drinks from fridge and put on table. After 10 minutes, you can see a lot of water droplets (condensation) outside the tin. Constantly like that, the moist will allow fungus to grow.

Also, if not in use, it is recommended to run the aircond at least once every 2 weeks or anytime you feel right.

Just my 2 cent.