The job carbon plays in a fish tank can be broken down into three main categories.
1) Organics removal. Most notably in this category would be dark or tea colored water from driftwood. Also removes the fishy smell from your tank. If your tank smells bad it means something is wrong with the tank. You want to be able to smell the tank so you can tell if something is amiss.
2) Micro nutrients. Including but not limited to ammonia, nitrite, nitrate. Too much of these in your tank can be a bad thing not enough can also be a bad thing if you got plans which utilize these micro nutrients.
3) Heavy metals. Most heavy metals in the tank are harmful. Some metals such as iron are beneficial to a planted tank.
During the carbon manufacturing process it is washed with phosphoric acid which then leach out into the tank water and is converted to phosphate which can accumulate very quickly an account for unwanted algae growth.
For myself the only time I use carbon is when company is coming over and I want to give the water a quick polish. I use a Fluval G3 so exchanging chemical cartrage are quick n easy.
I hope I have been helpfull.

I have carbon in one canister, been in there for over 12 months (1 whole canister tray). It no longer absorbs anything, as expected, but it also doesnt not leach anything back into the water, it is now no different to the matrix in there. Beneficial bacteria now colonise it. This tank does not have a problem with algae

It is an excellent water polisher, but only absorbs for around 2 weeks, then needs replacing if that is what you have it in there for. If that in a canister you will need to open and renew fairly often.

I like to use it in fry tanks, to keep the water 'sweet'

I think its more personal preference