You’re on the right track with the json_populate_recordset() idea. You can use it to unpack the json array as a plain set of address, then pack it back up into an address[] array using array_agg():

select array_agg(an_address) as array_of_addresses
from json_populate_recordset(null::address,$3) as setofaddresses(an_address);

Note that if you pass an empty array as $3 to the query above, it’ll have a null as the array_of_addresses. ARRAY() constructor syntax lets you plug a subselect into it, shortening that to:

select array(select json_populate_recordset(null::address,'[]') );

Which gets you an empty array in cases where $3 is an empty array, instead of the previous null.

Here’s an example:

create type address as (
    street_name text
  , street_no int
  , zip_code text
  , city text
  , state text);
create table subscribers (
    id bigint generated by default as identity primary key
  , first_name text
  , last_name text
  , addresses address[]);

prepare insert_into_subscribers(text, text, json) as
insert into subscribers(first_name, last_name, addresses)
values($1, $2, array(select json_populate_recordset(null::address,$3)) );

execute insert_into_subscribers( 'John'
                                ,'Doe'
                                ,'[ { "street_name": "Sesame Street"
                                     ,"street_no":3
                                     ,"zip_code":"432ABC234"
                                     ,"city":"New York"
                                     ,"state":"NY"}
                                   ,{ "street_name": "Lincoln Boulevard"
                                     ,"street_no":4
                                     ,"zip_code":"432ABC235"
                                     ,"city":"Albuquerque"
                                     ,"state":"NM"}]');
select*from subscribers;

select id, first_name, last_name, addr.* 
from subscribers 
cross join lateral unnest(addresses)with ordinality as addr;