We have unexplained infertility (sperm fine, ovulate regularly, good quality eggs). We've had 2 successful embryo transfers (and 2 unsucessful), so for us it could happen naturally and we will probably not use any form of contraception again, but I thinking would be incredibly unlikely.
I also didn't use any contraception with 2 long term partners over 10 years (obv. not at the start of the 2nd relationship so not 10 years solid) and it never happened. I think as much as you do find those stories of 'miracles' (and there is always hope and the possibility it might happen for you), there are many many stories of people for whom it just never happened. But those stories aren't as interesting and don't really get retold on internet forum threads: it's the 'friend of my sister who was told she'd never conceive naturally' stories that get shared because they are not the norm and they stand out in the memory of the teller.
In your position, I'd decide if I wanted to go down the route of continuing TTC in earnest with the likes of the sperm meets egg plan and whether that would put stress and strain on your relationship if you continued to be unsuccessful each month, or just not use any contraception from now on and decide if you can be content with 1 child if it just never happens for you, or decide if you want to try to save up for IVF with the risk of spending all that money and it still not working.
Infertility really really sucks and it's really unfair that we can't just have sex and make a baby. If hearing success stories about those who conceived naturally after fertility issues helps you to have some hope then that's great. And a lot depends on your circumstances, age, etc. If you're late 20s then you still have plenty of time to try again for a few years, then reconsider your financial situation. I just think it's also important to manage your expectations.
Very best of luck to you. I very much hope that you get that much wanted second child in the future.