Imagine Ladybird is developed and is successful. Lots of people use it to read websites.
But then Badcorp takes the code and builds their own varient with extensions. Badcorp is big and has lots of market share. Lots of people use Badcorps's browser, and because lots of people are using it, lots of web developers code for it, including coding for its extensions.
Soon, lots of websites -- including Badcorp's own websites, and they have lots of popular ones -- use the extensions in the Badcorp browser.
Then people still using Ladybird can't use it for most websites. They have lost something.
What if BadApple takes BSD and forks it. Then they make their own BSD with extensions that only works on their own shiny fruit hardware.
What have the original BSD users lost? Absolutely nothing. BSD still exists, it’s still maintained, and people can still use it. They can also use fruit BSD if they want.
The big difference is: how important is the software for interoperability?
With an OS core, interoperability isn't really important. Existing BSD users presumably weren't too interested in buying shiny new Macs to run their BSD OS on, so Apple using BSD as the core of their OS really didn't affect them. Moreover, existing BSD users didn't need to interoperate with the new MacOS users. An OS isn't some kind of network protocol. BSD users could work with MacOS users just like users of any other OS, using existing network protocols and other standards.
The poster child for the BSD/GPL argument on the GPL side is usually Microsoft's "embracing and extending" of Kerberos. It's a network authentication protocol, licensed with a BSD-like permissive license, and Microsoft infamously forked it, creating their own proprietary extensions. This resulted in only non-MS users not being able to fully interoperate with MS users.
We do already see cases now where web developers write websites targeting Chrome-only browser extensions instead of sticking with standards. In theory, if this happened with Ladybird, it should be possible for the original devs to simply add their own versions of these extensions, but how feasible that it I'm not sure. Currently, there's Chrome-only extensions which apparently haven't been implemented by Firefox for some reason, so maybe it's not as easy as it sounds.
But then Badcorp takes the code and builds their own varient with extensions. Badcorp is big and has lots of market share. Lots of people use Badcorps's browser, and because lots of people are using it, lots of web developers code for it, including coding for its extensions.
Soon, lots of websites -- including Badcorp's own websites, and they have lots of popular ones -- use the extensions in the Badcorp browser.
Then people still using Ladybird can't use it for most websites. They have lost something.