This is not a critical problem but a surprise. If a chest is blocked from opening with a non-transparent block then it does not receive items from/or give items to a hopper. I even tested this with a cat, which sits on top of the chest and also prevents items from entering-from or exiting-to hoppers. I can see that this might even be a feature with pistons, etc., but I discovered it when I was trying to make a compact structure and while I needed the storage that the chest provides, I didn't anticipate a need to open the chest so I blocked it with other parts of the device.
If you wish, go ahead and label this, "Works As Intended." But at least it should be noted in the Wiki.
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We have to wait for a comment of Mojang if this is intended or not.

Opposite of MC-7543.

After inventing things with hoppers for a week or so, I've decided that I like this behavior as a feature and I hope you don't fix it. A sticky piston can be used to stop the flow of items though a series of hoppers and chests and that might prove useful in a system. If trapped chest don't have this limitation (per MC-7543), all the better. Then we have a choice.

With MC-7543 beeing fixed I assume this is intended.

Why is this fixed if it is an intended feature via MC-7543 or are they just now deciding they are now just going to allow all chests to be hoppered out and in of?

If this "works as intended," then it would make sense to make trapped chests behave differently as KJP12 suggested. However, it appears that Mojang "fixed" trapped chests so as to behave identically to regular chests in this regard, taking away that choice.
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