If you put it as "are they necessary" my answer would be yes.
If you ask "Are they mandatory" then my answer would be a reluctant "No."
I've run tanks without them before, reefs, FOWLR, and nanos. I now run skimmers on everything. IMO they have advantages that are too numerous to ignore. First and foremost, the less crap in the water, the healthier your livestock will be. As far as the hobbyist is concerned, they remove junk from the water that you would have to remove through other means, such as media based mechanical filtration, water changes, etc.
Skimmers are not cheap - at least not decent ones - but if you are approaching a new tank setup and you start nickle-and-diming over the cost, you may want to consider downsizing your project to where you can buy all of the equipment to do the job right. I don't know if you are new in the hobby or not, but I can tell you that a skimmer is one of those pieces of equipment that makes saltwater fishkeeping much easier. Save yourself the challenges and headaches that come with skipping them.