If I do not remain relentlessly active, all people, O Partha, will be following my path by all means.
Krishna says his activity does not depend upon whether he needs it for himself. The greater consideration is whether his acting or remaining indifferent will be the right example for others, then and for ever. The crucial thought is what will be the right model for the world.
The answer is clear. If people see him given to inactivity, they will also take to the same course, shunning actions altogether. That would be totally against the laws and intent of Nature.
As he said earlier, the world is a revolving karmic wheel, and everyone is a cog in it. Being so, Krishna cannot afford to strike a different note. He remains immensely active to ensure the good of all. How well he instils the societal dimension in the individual mind!
Any adult should think of the whole society and contribute to its collective welfare. Selfishness must give place to selflessness and expansion. I-ness should leave and other- ness should take over.