Part of the stigma is the sheer number of well-meaning but unhelpful therapists. I went to several free and religious counselors when I was young, and had several worthless experiences.
Most of them just wanted to hear what I had to say, and had no advice, as though hearing myself talk about my problems would solve them automatically. A few gave suggestions but not things that would realistically help (Maybe you should try to be more social, to deal with your depression). Some put me into group therapy with people whose problems were much worse than mine, and this gave me the sense that my problems were small and not worth their time.
Having people goto therapy sounds nice in practice. In reality there are more problems in attending therapy than it promises to resolve, so you're likely to have even more problems than you started with.
There's a lot to unpack here... But let me touch on a couple of the points you raise - from the perspective of a trained, but non-practicing therapist.
First of all, there are lots of terrible therapists out there. Especially of the 'religious counsellor' variety (I'm shuddering at the phrase). I had a similar negative experience with a school counsellor who had an academic degree in psychology (which involves zero client hours) and had self appointed herself as a therapist in the educational context.
So choosing the right therapist is key. Well trained therapists with good experience are not free. Someone is going to have to pay for what is an expensive and highly educated professional service (for example it can take up to a decade to become a clinical psychologist here in Ireland). That might be government, charity, or client payment - or it might be that some excellent therapists offer a portion of their time at a reduced rate; but it's extremely unlikely that you'll get good therapy for free.
To address your second point however, I have to emphasise that the goal of therapy is not to give advice. It's explicitly antithetical to most schools of psychotherapy / counselling. There are many reasons for this - the therapist is there to be the one person in your life who doesn't evaluate you, people respond negatively to advice (with 'reactance') even when they desire it, advice isn't necessarily generalisable. But overall, if you're looking for advice you need to talk to a domain expert - e.g.: someone whose doing the job you'd like. If you're going through emotional difficulties, counter-intuitively the last thing that will help is concrete advice.
What the research shows is effective are things like the relationship between therapist and client, trust, tailored interventions (e.g.: CBT for PTSD or OCD) etc.
If you're ever interested in resuming therapy, I'd recommend reading more into how the different kinds of therapy differ. It sounds like some form of CBT might be useful for you - but above all the important thing is to work with a professional whose a good personal match for you. Picking a therapist is selecting someone with whom you'll be forming an intimate relationship, and compatibility is vital. So I'd encourage shopping around.
Counseling is mostly unregulated with practioners who have very little training. There's not much evidence base and what evidence there is is either weak, or suggests not to use counselling.
Modern (and I recognise some terrible practice used to happen) tries to have regulation through professional registration and protected names; and tries to work to an evidence based model.
I agree that therapy as evidence based treatment is fairly new and there there are still many terrible therapists.
Most of them just wanted to hear what I had to say, and had no advice, as though hearing myself talk about my problems would solve them automatically. A few gave suggestions but not things that would realistically help (Maybe you should try to be more social, to deal with your depression). Some put me into group therapy with people whose problems were much worse than mine, and this gave me the sense that my problems were small and not worth their time.
Having people goto therapy sounds nice in practice. In reality there are more problems in attending therapy than it promises to resolve, so you're likely to have even more problems than you started with.