If you reinvent a wheel you need to maintain that wheel. That is your customer's money. Money which can be put in features instead of striving to technical excellence.

Instead, you now put money and time in building a wheel for very little benefit (if you can feel the performance of jQuery, you're doing to much DOM operations and you probably wouldn't benefit much from stripping it out).

Some projects are not meant to last long-term, and jQuery would work just fine. Even if it is old fashioned.