This is probably more of a question for web developers working at Google, etc.
In general, there are tens of millions of devices running KaiOS so the user base is large enough to warrant some attention especially if you are targeting users in Asia.
Also, KaiOS does include an official Youtube "app" (fullscreen website) by default but not all KaiOS devices support over-the-air software updates.
It is rather likely that there is a legal agreement between the KaiOS owners and Google that grants KaiOS the right to use YouTube branding but also ensures Google do not break YouTube compatibility with KaiOS devices for a certain time period.
The same applies to Facebook, which is included as a standard "app" (fullscreen website) on KaiOS phones as well.
Finally, since KaiOS feature phones cater to low-end market segments, you cannot expect or demand that users pay to upgrade their devices since they might lack the funds to do so. You either test that your online service works on their devices, which might not receive software updates, or you lose them as users.
