No, your fears aren't warranted. In fact, when Apple launched their ARM SoC for their laptop / desktop platform, I pointed out that Intel / AMD x86-AMD64 processors are now the final bastion of computing freedom as they build
general purpose CPUs, and their current business model prevents locking it down to any specific platform.
With custom ARM SoCs we are going to see extreme platform lockdowns. (What most people here don't get, or are being deliberately obtuse about, is that ARM's IP are used to build System-on-Chips where the ARM processor is just one of the units. It is other custom parts of the SoC that allow you to lockdown and make the SoC incompatible with other ARM SoCs).
This is how Apple ARM SoCs only fully support ios / macOS, Google's will only support Android / ChromeOS, Microsoft's ARM SoC will only fully support Windows etc, and will enforce platform lockdown.
To understand why this is happening, we have to recognize the shift in the business model of BigTech - They want to turn everything into a service that will earn them recurring revenue. Platform lockdown will ensure they can force users data on to the cloud by pushing cloud services on these device and limiting their hardware. While initially they will lock down personal data too on to their specific cloud services, regulation may force them to allow "data transfer" between the BigTech services to give consumers the illusion of choice.
Remember, PRISM has showed US government how valuable it is to have access to personal data from corporates and how easy it is when it is on the "cloud". BigTech's worldwide reach will allow them to literally spy on anyone in a few decades and the US needs that ability to maintain its influence on world politics.
I predict a very bleak future for personal computing, where the concept of ownership of computers or computing device will no longer exist - your device in the future will be fully controlled by the BigTech, and we will have no computing freedom to even install any open source code on "our" device.
BigTech is already experimenting with "cloud coding" - this means they will even have access to all your codes in the future too - in such a scenario no competitor will emerge in the future to be able to dislodge them for centuries until they lose political backing.