Luckily you are not the one that gets to decide what LN is for and what not. If people want to do this "stupid" messaging they will close all channels with you and route around. People like you are the reason why we need censorship resistance.
Unfortunately there is no way for routing nodes to discriminate chat messages from ordinary payments because the payload is encrypted. And routing nodes also cannot discriminate based on source or destination of the message since neither of those is apparent either. The only viable resolution of this issue is going to be requiring payment for message routing up front rather than only upon a successful end-to-end payment.