For public-domain piano pieces, you don't have to typeset or export anything yourself — ten external sources cover most cases, split into two groups.
Link collection: sheet-music sources
All these sites open externally. Sources with MXL/MusicXML files import straight into Klavissimo; PDF sources need a detour — how, is covered in the linked article or the MuseScore export.
70+ beginner classics as ready-made .mxl files, no account needed — including Für Elise at several difficulty levels. The source behind “Discover”.
Huge catalogue of community scores, downloadable as MusicXML with a free account.
Editorially engraved editions (songs with piano accompaniment, string quartets), freely available on musescore.com.
All Mozart piano sonatas, complete, as MusicXML — maintained as a research corpus on GitHub.
Not a sheet-music archive but a directory: links to further sites with MusicXML downloads.
The largest library of public-domain sheet music, mostly scanned original editions.
Around 700 piano pieces, public domain or CC-licensed — as LilyPond, PDF and MIDI, no MusicXML.
Public-domain sheet music as PDF, plus free recordings to listen to.
Free, public-domain PDF sheet music with multilingual search.
A large mixed catalogue with many free PDFs — quality varies.
Good to know:
Copyright in short: compositions whose protection term has expired are public domain — free for you to use. Purchased or current scores (including individual arrangements on musescore.com) carry whatever licence is stated there instead. This isn't legal advice.