Depends on your definition of "better". If you mean "better teacher", you'd be correct in a research university, but a professor who is good at getting grants generates a lot more revenue than they cost.This depends on how you do the accounting. Grant revenue is not fungible, and while the value to the institution and the state of big grants is indeniable, it still requires extra revenue from elsewhere in the institution to service the grant, so if the general funding of a university is tight then a researcher with a big grant will end up sucking resources out of other parts of campus, often off the backs of undergradutes. This has been exhaustively studied, especially since the 2008 crash, by people like Chris Newfield. This excellent blog post (and the earlier one it references) explains some aspects of the problem.
The bottom line is that a researcher in a research university with good grant support is serving the fundamental mission of the institution, and should be proud of the work they are doing, but they are not self-supporting no matter how big the grant or how high the negotiated overhead rate. (Nor should they be!) - DvF