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Yes, most office ‘productivity’ suites already do this, and save their documents along with stylesheets, images, etc in a Zip file:
Libre Office, OpenOffice, and NeoOffice (Mac) have been saving their files as XML by default for many years (.odt, .ods, and .odp file types are all Zip files). The packages are essentially variant implementations of OpenOffice, and all comprise a wordprocessor, spreadsheet, presentation software, and a vector drawing program, and they share related Schemas. The Office Document Format (ODF) was the first official International Standard (ISO/IEC 26300) for office documents. All of them can read and write Microsoft Office files.
Corel's WordPerfect suite has shipped with a fully-fledged XML editor for many years (which also does full SGML as well). It can save the formatted output as a Microsoft Word .doc file, but it uses its own stylesheet technology to format documents, not XSLT2 or CSS. It can also save its own (WordPerfect) document format to an XML representation.
The AbiWord wordprocessor (all platforms) can open and edit Word and OpenOffice documents, but it can also save them in DocBook XML or even LATEX format (although it does not provide native XML editing) which makes it an excellent converter.
Microsoft Office 2003 provided a ‘Save As…XML’ to all parts of the suite except Powerpoint, using WordML to represent the visual appearance of the document, although it will preserve style names if they are in use.
Office 2007, 2010, and later all save natively as XML documents (.docx, .xlsx, and .pptx file types, which are Zip files). They use Office Open XML (OOXML, similar but unrelated to WordML) which is Microsoft's equivalent to ODF. It is a parallel ISO standard.
Word 2003 shipped with a real XML editor as well, supporting other W3C Schemas as well as its own (but not DTDs), and this also provided a method for binding element types to Word's named styles (like Microsoft's earlier product SGML Author for Word did).
Avoid Microsoft's ‘Works’ package, as it is incompatible both with XML and all other Office software.
I have no information on Lotus office products.
There is more detail under ‘XML File Formats for Office Documents’ in the XML Cover Pages which briefly describes and points to further information on: GNOME Office, KOffice, Microsoft XDocs, OASIS TC for Open Office XML File Format, 1DOK.org Project, and OpenOffice.org XML File Format.