Issued patents have already undergone an examination by a patent examiner, who found that the patent met the statutory requirements for validity, so it seems reasonable to me that someone wishing to overturn that decision should bear the burden of proof.
On this point I've been informed by patent lawyers that at trial something like 2/3 of patents will be found to be invalid. The problem is that nobody knows ahead of time which of those patents will be found to be invalid.
Unfortunately the examination process doesn't seem rigorous enough for this to be the case. This is where greater effort and strictness should be applied.