The third party should be permitted access only under carefully controlled conditions, for instance, a court order.
Thus far, no system design has been shown to meet this requirement fully on a technical basis alone.
On a national level, key escrow is controversial in many countries for at least two reasons.
Many countries have a long history of less than adequate protection of others' information by assorted organizations, public and private, even when the information is held only under an affirmative legal obligation to protect it from unauthorized access.
Another is technical concerns for the additional vulnerabilities likely to be introduced by supporting key escrow operations.