RESEARCH: Most of the keywords I researched have zero volume traffic per month. The ones with traffic are very competitive and are more general terms (e.g. copywriter or freelance copywriter). Is there any point targeting key words with little or no traffic? And if not, then what should I do?

Ideally you want a mix of high volume, medium and low volume keywords.
Assign the high volume to pages higher up in your site architecture as they have the best chance of ranking.
Don’t underestimate low volume keywords, you can ‘own’ these phrases. Even one or two searches a month will add up over the years.
Longer tail keywords tend to bring people in who are more in the awareness stage, so ensure you have ways on the site to collect their data and remarket to them. Remember to play the long game with SEO.