Geekbench 5 and 6 both correlated with SPEC scores at nearly 1:1. SPEC is the industry standard for CPU benchmarks. So in a way, Geekbench does what OP suggests which is a general measurement of performance. If you want to see specific areas, Geekbench shows sub scores.

Here's research done by Nuvia before they were bought by Qualcomm: https://medium.com/silicon-reimagined/performance-delivered-...

Since the loss of Anandtech, have any of the other tech websites started publishing SPEC results for systems they test?