I agree with @btraill here. Bedrock is a lot better than vanilla WordPress. It should be the golden standard in WP deployments if you ask me. But we're not there yet, as the adoption is so hard because it is more geeky than a traditional WP 1-click install. It requires a bit more technical knowledge and understanding of how GIT works, what is composer, how OOP PHP works, it requires basic terminal knowledge and so on...
@slimx and @jeff. Almost all plugins are compatible with Bedrock since most of them use the WP functions to determine the paths to the files. Having WP files in a separate folder is a basic WP functionality since almost the beginning of WP. Personally, I have only found a few (2 or 3 from what I recall) that were not compatible. All because of bad coding and hard-coded /wp-content/ paths. The last one I remember is FlyingPress (because of the way it optimizes static files) ... but it will add support for it soon.
@Derek - WP was created (2003) way earlier than PHP Composer was created (2012), and before Laravel was the way and the standard in PHP coding. Nowadays, the OOP / Laravel style of coding in PHP is normal, and it is here to stay for the long run. It only makes sense to adapt to the new tech. And Bedrock - style WP is the answer to this.
Unfortunately, WP is veeeeery.... slow to adapt to new tech and new trends. See page builders, for instance. They were created way earlier than Gutenberg page builder (which even to this day is not good enough and the world of page builders continue to grow)
Based on my years of experience, it makes a lot of sense to have your code GIT-based, not SVN or non-versioned at all. It makes a lot of sense to use Composer to optimize re-used code across multiple plugins and so on. Just look at how many plugins use Composer in themselves, which duplicates a ton of code and creates useless repetition and slowdowns in order to load all of this repeated code.
This can also be said about the coding standards - which WP has it's own, while all the industry adheres to the PSR coding standards.
So, in conclusion I fully support Bedrock and a native integration and support for it would be totally amazing. There is a lot of work to be done here, if true support is wanted, but basic Bedrock support, I believe can be achieved even now. Deployment can be done using a small PHP script which acts as a webhook for the GIT repo. Didn't tested Bedrock on Enhance, but I think it can be done. Manually, not via an installer ofc.