Totally, I get that. That's why BrowserBox is also self-hosted, and yes, has a Docker image, too! Not free nor foss, tho. But I do try to be flexible.
As to cloud - indeed, why would you want to trust a cloud provider with sensitive internal browsing? Also, providing a SaaS is a hassle, but I feel I must do it serve that side and enable those uses, some of which are cool.
Ohh I didn't realise that it's your product, sorry. It sounds interesting but I'm only a home user (in Europe with not much budget). I just use remote browsers now for navigating the complex patchwork of blocks in the EU. Some sites are blocked in holland, others in spain, etc.