Does the missing of header `Set-Cookie` break Nginx proxy_cache?

I have a Nginx proxy server for a Node.js service which reads multiple files and generates a response. I want Nginx to add basic caches for me:

upstream my_http_servers {
    server 127.0.0.1:7001;
}

proxy_cache_path /var/cache/nginx-combo levels=1:2 keys_zone=my_cache:10m inactive=1w max_size=200m;

server {
    listen 80;

    proxy_cache my_cache;

    location / {

        # %%%%%%%%%%%%% SPECIAL LINE OF IGNORING %%%%%%%%%%%%%
        # proxy_ignore_headers Expires Cache-Control Set-Cookie Vary;

        # expires    24h;

        proxy_cache_lock on;
        proxy_cache_lock_timeout 10s;

        proxy_cache_key $scheme://$host$uri$is_args$query_string;
        proxy_cache_valid 200 1m;
        proxy_cache_valid any 5s;
        proxy_cache_use_stale error timeout http_500 http_502 http_503 http_504 http_429;
        proxy_read_timeout 10s;


        add_header Access-Control-Allow-Origin *;
        add_header Access-Control-Expose-Headers "X-Log, X-Reqid";
        add_header Access-Control-Max-Age 2592000;

        proxy_set_header   X-Real-IP $remote_addr;
        proxy_set_header   Host $http_host;
        add_header X-Proxy-Cache $upstream_cache_status;

        proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
        proxy_set_header X-Forwarded-Proto $scheme;
        proxy_pass         http://my_http_servers;

    }
}

I tried to pressing test it with wrk and it always responded with X-Proxy-Cache: EXPIRED or X-Proxy-Cache: MISS, which caused heavy pressure on Node.js since there are too many requests missed the cache.

Then I also tested it on Chrome, and surprisingly found X-Proxy-Cache: HIT was generated after a first response.

So I guessed the difference in the HTTP headers from wrk/curl and Chrome caused the difference. After some attempts I found Set-Cookie: ... made the difference, and it could be so solved by proxy_ignore_headers Set-Cookie to ensure Nginx has constant behavior on both sides.

And the question is why? Why Nginx handles requests with/without Set-Cookie: ... differently? What's happening when Nginx is deciding whether or not to use cache?