In all of the cases so far, one thing is clear: The goal of using a blockchain is to raise the level of trust participants have in the network and the data it produces—ideally, enough to be able to use it as is, without further work.
Reaching this level of trust is possible only if the software that powers the network is free and open source. Even a correctly distributed proprietary blockchain is essentially a collection of independent agents running the same third party's code. By nature, it's necessary—but not sufficient—for a blockchain's source code to be open source. This has both been a minimum guarantee and the source of further innovation as the ecosystem keeps growing.
Finally, it is worth mentioning that while the open nature of blockchains has been a source of innovation and variation, it has also been seen as a form of governance: governance by code, where users are expected to run whichever specific version of the code contains a function or approach they think the whole network should embrace. In this respect, one can say the open nature of some blockchains has also become a cop-out regarding governance. But this is being addressed.