Items like wood blocks and crafting tables cannot be set directly on carpets. Doing so puts the blocks one block above the carpet. It may be a good idea, if putting a block were a carpet is, to remove the carpet as the block is placed.
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Carpets require resources to create, so it's for the best that they aren't removed in the same way snow or tall grass is when placing a block in their space. They could make it "break" the carpet and drop as an item when you place a block on it, but I don't believe any current block behaves that way.
Why not do it like how wool blocks have different damage values to represent the color? This time, the damage value not only represents the carpet color, but also
the block ID of the block that is placed ontop the carpet. This would be nice except the fact that the top pixel of the block placed ontop the carpet will overlap with the block above it.
Blocks placed in the world only have 4 bits to store extra data. Carpet already uses all 4 bits to store the color. Storing block IDs requires 8 bits. In order to store that extra information, carpets would need to be a tile entity, like a chest or a furnace. This would be a performance hit, considering how many carpets you are likely to use to cover a given area. There's also the issue of placing a functional block, such as the aforementioned chest or furnace, on top of the carpet. It would be difficult to make them still function, and store their data.
The simple answer is to just remove the carpet and place the desired block. It will look about the same.
2 blocks cannot occupy the same space.