In modern CPUs registers are a high-level abstract concept (see register renaming), so writing to a register doesn't have any specific location to overwrite. R

In modern CPUs registers are a high-level abstract concept (see register renaming), so writing to a register doesn't have any specific location to overwrite. Recent Zenbleed vulnerability was an example of that — clearing of a register was setting a temporary boolean saying it's zeroed instead of writing actual zeros.