From my point of view, this seems to be one of the biggest barriers to widespread Bitcoin adoption. One of the most widely cited benefits of Bitcoin is that it is trust-free and you are in control of your own money.

But the vast majority of people don't have the technical ability to store their own bitcoin. Even many of those who can are still putting inherent trust in the system if they don't understand exactly how it works. How do you feel about being entirely responsible for huge sums of money like your life savings? If you fall back to trusting a bitcoin bank for this anyways, then there is little incentive to switch.

Now of course you can say that the current system also requires a great deal of trust on many levels (banks, government, etc.). But I think most people are more comfortable trusting an established system (especially in developed countries where it more or less is working) than something brand new that  they don't even understand. There has to be some other incentive to use Bitcoin to get a majority of people using it and only then will trust develop.

Moreover, it seems to me that the countries that need Bitcoin the most are the ones where it is least likely to gain ground. Example: Argentina. There is a huge amount of inflation (25% annually), nothing is being done by the government, and there is zero confidence in the banking system - most people don't have bank accounts and literally store their life savings in USD under their mattress.
But why would people who barely trust the banks trust someone trying to sell them on Bitcoin - something they don't even understand? Third party services and banks that simplify payment and storage will always be necessary and people have no reason to trust them. Even if you can create something that the user is in control of (hardware wallets, etc.), a non-technical person is still putting trust in you since they have no knowledge of how the system works.