Judicial systems have to deal with three sets of people: the provably guilty, the provably innocent, and everyone else. It’s not hard to deal with the first two groups: lock one up, let one go. The burden of proof is a tool for figuring out how to treat the third group.
If the burden of proof lies with the accused (if s/he is guilty until proven innocent), then the ambiguous cases will end in conviction. This leads to unprovably innocent people spending time in jail, while guilty people walk the streets (since the person who committed the crime in question isn’t tried for it.)
If the burden of proof lies with the accuser, and the accused is innocent until proven guilty, then everyone but the provably guilty walks free. The result is that (in theory) only guilty people spend time in jail, but some guilty people get off.
We hate to see people who we think are guilty get off. But do we hate that more than we hate seeing the innocent locked up? OJ Simpson or the Guildford Four?