I'm very sorry to hear you feel that way about our support team. While I fully understand your frustration (Its frustrating to myself when I have an issue I cant resolve), let me explain the situation from a support standpoint, in terms of your own site there.
At present you have 19 applications which were not written by our team (3rd party), and 23 plugins. Any one of these could be causing issues on your site in various locations. You mentioned there about troubleshooting, and indeed switching these off for any developer would be the very first course of action in determining the cause of an issue. These 'hook' into 213 locations within our core code, and therefore can very much affect how things work, and cause bugs. We very much wish that wasn't the case ourselves, but unfortunately this is the case if you run modifications to your site.
In addition to the above, while looking at your system in an aid to troubleshoot the issue, we would look at anything which may be 'likely' causes. You have many items which are out of date. That not only can lead to issues, but is almost certain to. Many updates are done so in order to resolve bugs, so you are actually running code known to be broken in most cases. We look at system logs, of which you have 11 pages of in 30 days. Usually that would be expected to be empty.
We then have cloudflare in the mix. This, in addition to setup issues server side and 3rd party code issues, is one of our highest causes of issues on self hosted platforms. Its only sensible to ask that this is switched off.
The above being said, at no point have we stated we will not look into your issue, and at no point have we stated the issue 'is 3rd party'. What we actually asked is that these things are checked first, before we continue with our investigation. There has been no further response on the ticket since that point.
To use your own analogy there. It's like you visit a doctor for a headache, the receptionist seeing you have blood running down your head one side, a hole in the other side, you have a hat which looks to be too tight and crushing your skull, and the nurse saying "Before we continue, we need to check the obvious. We need to remove that hat, patch that hole, and check to see where the bleeding is coming from". Unfortunately, that nurse is not going to send you to the doctor before performing her preliminary assessments and checks.
We're certainly not here to work against you Guarav, and again, I'm personally sorry to hear you believe we are. It's very much in our interest to ensure your issues is resolved as quickly as possible.