The current algorithm for hot questions does not take into account whether a question was closed. Given that closed questions are typically off-topic or low quality, IMO they should receive significantly less weight in the algorithm. Quite often on the smaller sites, egregiously off-topic questions attract a flurry of attention that pushes them near the top of the hot list. Once the question is closed, views rapidly plummet. Having the "hot" list polluted by closed questions makes it less useful for finding out what others are still looking at and talking about.
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I think there's a misconception here -- closing does not mean "get this off my screen ASAP", closing means, "this question should be re-evaluated by the community".
That is, it should be edited, improved and salvaged if at all possible.
Suppressing a question the very instant it is closed would not serve this purpose.
I'd also argue that, as you said,
So there is "enough" evaluation of closed questions, but suppressing them further would not be helpful.