I found this bug where comparators dont output any signal from a chest, when the chest has a block on top. I'm not sure if it's intended, but I thought I might as well post it. It allows for a cool clock like in the third screenshot, However the clock creates major lag spikes on servers after 1 minute or so, more lag than it should.
Since I don't seem to be able to upload screenshots, I uploaded them to imgur:
http://imgur.com/advoWtp
http://imgur.com/Fyh17O0
http://imgur.com/9q6GdZb
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thanks ^^
It seems like this has been fixed, see the new screenshot.
This issue has not been fixed as of 13w07a. My set-up is shown in two new pictures. The chest is half-full so the comparator should be lit, which it is when the chest is not blocked from opening. Next I place a block above the chest and the comparator remains on. But if I force the comparator to update by momentarily applying a signal to it's side the lights go off and stay off. When I remove the block above the chest the comparator output remains off until I either push the button again or simply open and close the chest; then the comparator lights up again. Because of the long redstone path, pushing the button when the chest is not blocked makes no difference because the low signal strength from the button is less than the signal from the half-full chest. Pushing the button only serves to force the comparator to update. (The screenshot from 05/Feb/13 makes it appear that the problem was fixed but it might simply be that the comparator has not updated.)
Confirmed to still occur on 13w07a with all block updates (not just redstone). Reopened.

Is this now WAI because hoppers also can't interact with blocked chests?

Confirmed in 1.15.2 and 20w21a.
Still an issue in 1.16.1, items can go into a chest via hoppers when a block is on top, but items can't be detected inside a chest when a block is on top.

@unknown, that is MC-100302.
Can confirm in 20w48a.
Attached screenshots to issue.