Service workers can get wiped on hard refreshes or due to space constraints. And they are not easily transferred to new devices, unlike packaged applications. They're not a security mechanism.

And it does not necessarily address the compromise of the hoster either, since the attacker who has control over that may also have access to the signing keys. Especially in the case of a court order.

That effectively is a silent, user-targetable auto-update of software to which you entrust your secret data.

Auto-updates for crypto software should be verifiable through other channels, require user confirmation and use a distribution method that is difficult to scope to a single user to make targeted attacks harder.