Considered this for the three years I was on herbs, and yes, it is dangerous... If you don't mitigate it or expect your doctor to do everything for you. I don't think it's as dangerous as people make it out to be if you care about your own health, but it's definitely something worth noting.
I live in a place where trans care exists but where it's socially viewed as weird, it's hard to get care and even if I could, I'd be having to obey all doctors orders and I'd go bankrupt with medical costs in this country.
I view my approach as risky but mitigatable. In my eyes, a doctor is just someone with more knowledge and tools. I've spent many years reading up anecdotal reports here, scientific reports, fantastic trans resources provided by educational foundations, and learning about every single thing that can happen and what to do about it. By educating myself of the risk factors, what to watch out for, I've been able to know exactly the signs of anything bad happening. Check my breasts for lumps, every day. Stand up, exercise, make sure I don't feel tingling or spasms in my legs which might be dvt, cut sugar out of my diet, cut out fast food, in... A strange way, I've become far healthier because I put myself under the gun of a risky task, educated myself, and became hyperaware of all the bad things that can happen to my body. It's made me feel so much more confident that I can do things if I dedicate much time and effort towards them. It's made me healthier because I finally had a reason to care about my health. It's motivated me to care about my body, because I like it. Without transitioning, I might still be eating fast food and be on my way to cardiovascular problems.
I still reccomend getting blood tests fairly often, if you can. I'm slow on mine and get one a year usually. But I've been perfect on all levels every time, except slightly high testosterone and slightly low estrogen. But I feel I've fixed that.
As Didi said, it was either do it myself, or live the next 10-15 years in a version of myself I'm not happy with. If the situation arises, I would love to get on proper care. If the job situation in this country improves, if Healthcare improves. But I am not waiting for politicians and big business to decide when I get to transition easily. I'd rather put the risk on my shoulders than wait until I'm older and I've lost most of my growth hormone, and lived many years unhappy already.
It's not easy, but I think the struggle improved many parts about me, besides my body and self image. It's taught me I can climb the rockiest mountain safely if I learn about it and dedicate myself fully to doing it.
Also, at least in the US, it's illegal only to force people to buy overpriced, us produced, identical to everywhere else drugs, to line the pockets of big pharmaceutical companies, I sincerely doubt it's to protect consumers in any way, although they'll tell you it is. Look at what we've done to insulin. It's instead to force you onto one or two brands of expensive estrogen.
But yes, if you expect to just start taking estrogen and an anti androgen and don't put the effort into learning what can happen and don't put the effort into your own body, things can go south. In this way, we become our own doctors.
Things can happen bad if you don't care about your body and expect your doctor to do everything too.