Currently, I export as a HTML5 website, then fire up filezilla, then ftp up the locally exported game to a public test server. I do this a lot.
It would be very handy (but not high priority) to have a "FTP HTML5 web site" option in the C2 exporter to save this step. Dreamweaver for example has this, and I use it constantly.
I could live with only one FTP site being defined at a time, but obviously a fuller solution would be to:
1) allow multiple ftp sites to be setup (dev and test for example).
2) allow passive or active
3) allow non standard ports (I dont use this but someone might)
4) possibly handle SFTP (much more work and dont know how many people use this)
It would be fine to transfer everyting in binary mode.