I see what you mean, it's just i think it would put the UK and other 'Safe' countries in a difficuilt position.
If you could renounce your citezenship, then it would make removal of a person extemely hard. A lot of people would be doing it.
I'm not sure, but I don't think the convention would cover people who voluntarily make themself stateless, just those who have been made so for reasons beyond their control.
Also, if you have claimed asylum the ZWE may not want to talk to you and therfore it would be very hard for a ZWE national to do so.
Also, it may have implications for your family back home. Contacting the ZWE authorities extensively may go against you in terms of your credibility.
I'd speak to an Immigration Lawyer, a list is available from the OISC website (
http://www.oisc.gov.uk/).
J