Forward thinking venture capital funded companies are getting rarer, hence the question on motivation. Especially the last few years many VC Foss companies have squeezed harder the other way (gitea, Terraform, docker). So all kudos to BitWarden for launching Lite.

What you say a about brand dominance, or brand protection makes a lot of sense. It’s not a good look for them that a large number of people choose to use an unofficial implementation instead of theirs. And should there ever be a catastrophic security issue with Vaultwarden, it would still reflect bad on BitWarden as that kind of nuance (like “unofficial server side implementation”) tend to get lost in reporting. Having more IT workers self-host official version probably also helps pave the way for bringing enterprise-bitwarden to companies.

Valve are a bit of a unicorn though, because they are privately owned. There’s no investors demanding ROI the next quarter, which gives them freedom to think long term.
When Microsoft launched windows8 and the Microsoft Store, Valve took that as an existential threat to their whole business model (the Steam store). Valve feared that Microsoft was trying to position itself like Apple on iOS and Google on Android, where there is only one platform store, and all apps are purchased through the platform store, and the platform store takes that sweet sweet 30% cut. So Valve pivoted to ensure the Steam store would not be obsolete, and give customers a reason to still use the Steam store. And what they achieved is awesome, for Linux, for Valve and for gamers. But it took nearly a decade, which is a level of patience few companies have.