To OP: There are good reasons to add a carbon source to your system, and bad reasons.
Bad reasons: because you heard that it feeds coral and improves colors or polyp extension, or because “everyone else does so”.
The second bad reason here is obvious and true to any aspect of the hobby, and I always want to believe people at least have some reasoning behind their actions - but unfortunately that’s not always the case, so I’m adding it here as a wildcard.
The first reason though is because one needs to understand where these claims are coming from - and as already been mentioned here, it is not directly attributed to adding a carbon source, but rather to the way it affects other aspects of the system.
Not all system will benefit from this, some will destabilize and lead to the exact opposite.
Good reasons: To mature a young system during cycle, to fix an ongoing bacterial issue such as a Dino outbreak together with dosing bacteria, and the most popular one - to control either Phosphate or Nitrate.
If you do have a good reason, I would say go for it, but first see if you really do need it - for example for nutrient control many reefers do have enough carbon source already in their system, but instead lack either N or P to make the other one decrease. Adding a Carbon source in this situation would only accelerate the already on going trend, will bottom out one of the nutrients and won’t be able to go any further unless you’d start also dosing the limiting element (N/P).
In my main system I’m a heavy Carbon Source user, been using it for probably around 5-6 years if not more, I’m not dosing it, but rather have a permanent Carbon Source in the form of a Biopellets reactor.
This is an aggressive method to provide a carbon source and if left alone - does indeed bottoms out Nitrate. However, my goal with it is to lower Phosphate, and thus I dose Sodium Nitrate to keep the process going. The benefit of having it contained in a reactor (in addition to the fact that it’s required by how the media works), is that I’m able to control where the effluent full of bacteria goes - and this can be used to significantly accelerate the export of excess bacteria by directing it right into the skimmers intake and allow an agrasive method like this to work without causing bacterial blooming.
You asked for a photo - this is my 17 years old main system (tank have been upgraded over the years, but the content is the same):
And here is my other system, which I haven’t been intentionally adding a carbon source to, however I’ve been dosing it with Ammonium Carbonate, as well as Trisodium Phosphate to avoid bottoming both:
Growth rate is the same between the 2 systems, colors are very similar as well and depend more on light conditions than anything else.
Edit: typo.