How to deal with Support Issues?

I work for a big Cloud Engineering team.

They have been moving our support team out of the US to cost efficient centers such as India, Romania and Philippines. This means support teams can open a case with Engineering directly with little or no technical information:

We currently have a huge case load with very poor escalations. (Not enough information, lack of troubleshooting, little expertise from support teams)

Today we enforce a template to be filled before opening a ticket which is mainly ignored.

We also have account team members (mainly sales teams) opening tickets with us with no technical details under the excuse that is a big customer willing to spend $$$ and bla bla bla. Also internal people opening cases with no care for technical details but direct access to ping Engineering members.

This means our on-call get bombarded by support tickets and we can miss real issues because of the high and low quality amount of cases. I have though of the following:

Restrict who can open the cases: Only tech leads from support teams No internal people and force them to go through an alias or general chat with no SLO

Any other ideas?

How to start the conversation with support teams to get better response as I'm pretty much saying they are not doing their job.