If you can't automate this step, you have to read the insults, and pleading, and jerk-faced comments from the demanding users. Which takes time and energy.
And, look, that's not perfect and I'm not saying that it's not unpleasant. I'm saying that it's materially different from every person who uses your service costing you actual dollars. And if you can't see that, I honestly don't know what to tell you.
Go one step further and make it a product. OP'll be a millionaire in no time.
SAAS with free tier does it this way:
* To contact support via non-app method you need a PIN. PIN is displayed when you login into your paid account. Don't have a PIN? Can't connect to support.
* To contact support via app method your profile needs to be associated with a paid account. Don't have a paid account? Can't contact support via inapp