Randomized benchmarking protocols have become the prominent tool for assessing the quality of gates on digital quantum computing platforms. In `classical' variants of randomized benchmarking multi-qubit gates are drawn uniformly from a finite group. The functioning of such schemes be rigorous guaranteed under realistic assumptions. In contrast, experimentally attractive and practically more scalable randomized benchmarking schemes often directly perform random circuits or use other non-uniform probability measures. An important example for such a non-uniform protocol is linear cross-entropy benchmarking. The theoretical understanding of non-uniform randomized benchmarking is still an ongoing effort. We present a new extension of general theoretical guarantees for randomized benchmarking to non-uniform measures. Combined with results on random walks, our results identify experimental parameter regimes where one can guarantee non-uniform randomized benchmarking protocols to work reliably. One main motivation for the new guarantees is the development of trusted and efficient randomized benchmarking schemes for analog quantum simulators. We discuss how the framework of non-uniform randomized benchmarking can be applied in the context of bosonic and fermionic analog quantum simulators.