Filtered neighbourhoods typically allow motor vehicle access to all residences; you just have to use the designated route(s).
For many decades, housing estates have been designed like this anyway and millions of people live in cul-de-sacs without having any fear of dying because an ambulance or fire engine won’t be able to get through.
Information from healthcare trusts shows that schemes do not delay ambulances. In any case, emergency services are always consulted before any modal filters are installed.