Kernel Address Space Layout Randomization (KASLR) has been repeatedly targeted by side-channel attacks that exploit a typical unified user/kernel address space organization to disclose randomized kernel addresses. The community has responded with kernel address space isolation techniques that separate user and kernel address spaces (and associated resources) to eradicate all existing side-channel attacks. In this paper, we show that kernel address space isolation is insufficient to harden KASLR against practical side-channel attacks on modern tagged TLB architectures. While tagged TLBs have been praised for optimizing the performance of kernel address space isolation, we show that they also silently break its original security guarantees and open up opportunities for new derandomization attacks. As a concrete demonstration, we present TagBleed, a new side-channel attack that abuses tagged TLBs and residual translation information to break KASLR even in the face of state-of-the-art mitigations. TagBleed is practical and shows that implementing secure address space isolation requires deep partitioning of microarchitectural resources and a more generous performance budget than previously assumed.