Sure, it’s not life or death but your clients are definitely worse off than if you’d just taken the time to learn ES6.
Not knowing ES6 also just makes your life harder if you adopt other new JS advancements. For instance, it’s harder to look at the docs and examples for React and it’s related libraries. It’s harder for you to adopt Flow or TS.
Lastly, it should be especially easy for you to pick up ES6 if you know ES5 inside out.
Syntax? Get over it! Languages evolve. Syntax evolves. Refusing to update with the times ultimately hurts you more than your clients, as it dulls your skill set.
As a developer it's important to stay up-to-date. Sometimes this isn't possible due to slow to update libs or technical restrictions, but to solely write ES5 due to preference is avoiding a small amount of learning for convenience.
So, I would lean in the direction of it being irresponsible due to code being less easy to grok and harder to bring new people into the codebase.