ROLLING BASIS

When a firm recruits on a rolling basis, it simply means you should consider prioritising those apps.

Think about it - If you REALLY wanted to work at a firm, like you say you do in an application, then you would ensure you have the best chance of being offered a job. That means, in the case of firms who recruit on a rolling basis, applying early. It incentivises candidates to prioritise them.
 
Should the 'rolling basis' approach automatically stop me from applying because it seems a bit unfair and paves way for luck to creep in?

If a firm recruits on a rolling basis, they still have a set of standards candidates need to meet, so there wouldn't be any unfairness or luck to it.