After reading the comments here, the paste does indeed work the second time. Normally, I trust my Ctrl+V so I didn't bother a second time and concluded it didn't work. I asked my colleague to paste something in 0ad (without telling him the workaround) and he concluded also that it didn't work either.
To summarize, it works with a workaround. Even though the workaround is simple, it is not trivial/guaranteed that people discover it and therefore conclude that cut-copy-paste is broken. So, it does need a fix so that it works the first time.