Not for the first time, you've posted a question that refers to something we can't see. i.e. you've mentioned 'these tensions' but not told us which tensions you're referring to.
However I'll assume that this question relates to your other one and therefore that the tensions mentioned are those between individual rights and governmental rights.
Examining your list of possible people to decide such matters one by one . . .
'The public' can't decide because
(a) there are likely to be divergent views among the public as a whole ; and
(b) those who argue for individual rights to prevail are likely to be 'the public', who would therefore be biased in any decision making process.
Similarly, elected official can't decide because they make up the governmental authorities, at either state or national level, and will therefore be biased towards governmental rights.
The police can't decide because the role of any police force, anywhere in the world, should always be to enforce laws but never to determine them. (Otherwise you risk ending up with a 'police state').
That only leaves the courts. While courts should never be allowed to make laws, it's their duty to
(a) interpret them ; and
(b) ensure that they conform to constitutional provisions and/or human rights.
They're therefore ideally suited to the type of decision making that your question refers to.