I don't like being transgender being thought of as a mental illness, but the way it effects one's life often demands the help that counselling and other resources can offer.

Exactly this. There's no easy answer.

"shrinks" are involved to stop people from making the wrong decision. Many people who believe they are ready for HRT and SRS actually are, but some aren't, some look to transsexuality as a form of escapism and that will lead to intense regret and possibly self harm or even suicide later on. This doesn't effect how they choose to live, you can still do whatever you can to pass without HRT or SRS if your therapist deems you not mentally ready for the transition.

I know someone personally who griped for years about not being allowed by their therapist to get testosterone, only for them to later decide that they were genderqueer and were fine with their body. They're a bit... mentally unstable. I completely understand why they were turned down. In the end it was for the better. A good "shrink" will be able to tell pretty easily if you're mature enough and have done enough self discovery to confirm your dysphoria and need for a transition, it's not a problem, they don't stop people who legitimately are transsexual from transitioning.