1) My workaround
Add an empty paragraph before the table > select both > Ctrl+X > Ctrl+V.
2) Documentation
→ Writer Guide, Published 16 February 2012. Based on LibreOffice 3.4.5.
Chapter 9: Working with Tables
Moving a table (page 24)
To move a table from one part of a document to another part:
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Click anywhere in the table.
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From the main menu, choose Table > Select > Table.
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Press Ctrl+X or click the Cut icon in the Standard toolbar. (This step removes the contents of the cells but leaves the empty cells, which must be removed in step 6.)
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Move the cursor to the target position and click on it to fix the insertion point.
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Press Ctrl+V or click the Paste icon in the Standard toolbar. (This pastes the cells and their contents and formatting.)
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Return to the original table, click somewhere in it and then choose Table > Delete > Table from the main menu.
3) Bug Report
→ Bug 40893 - Drag and drop complete TABLE (contents) leaves empty table behind
Status: RESOLVED NOTABUG REOPENED (see @Pedro1’s comment below)
("…feel free to submit an enhancement request if you can provide a
conclusive concept…")