> I've always wondered why nobody suggests doing that in the US
In this case, Occam's Razor beats Hanlon's Razor: The simplest explanation is malice, not stupidity. The groups who are the most hysteric about hypothetical voter-fraud are dishonest. Their actual goal is not to prevent vanishingly-rare crime, but to suppress legitimate voters in a partisan fashion.
Finger-inking at the poll-site does not offer them a useful tool for skewing the election results. It imposes no special discouragement or advantage to a particular group, and it also does not create a system for arbitrary "enforcement." (In contrast, consider poll-taxes or name-similarity databases with insanely high rates of false-positives.)
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Some might retort: "I don't suggest finger-inking because it won't stop someone from impersonating another voter." True, it won't stop that from happening the first time, but it limits it to once. This means N improper votes require N humans, and as N gets large the odds of keeping it secret go to zero.