So Kirk's Enterprise was definitely NOT the biggest thing Starfleet had. it was the biggest and best ship sailing solo on independent operations. But bigger, better, more capable battleships (with tighter leashes), bigger, better, more capable research ships (with watchdogs), and other types should also exist.
That's the way I see it as well. It was Kirk and the unique gestalt he had with his crew that made the Enterprise the best ship to send to a crisis, not the actual ship itself.