It's not doing Save As that bit people. Think of a .doc file as a bad database format. It gets lots of in-place overwrites, and fragments of old versions stick around.
Right, OLE documents are comparable to read/write filesystems inside a file. The only mechanism given to make sure it is sparse was to create a new filesystem by having the application walk the existing one, basically a copy-based garbage collection.
Powerpoint files can be megabytes larger due to unused graphic artifacts; Word documents may contain older revisions of the text that contain deleted sections. Other things like the MSI installer file format are also OLE documents.
Microsoft eventually made Save in Office apps always create a new sparse filesystem to prevent these problems.