I wouldn't rely on Unity if I really target for the web. Whenever you hit problems about WebGL or Canvas, it's much easier to resolve with Phaser or another HTML5 framework. Web is hard in itself, thanks to modern browsers with different engines.
In my last workplace we had restrictions for each project like: not having more than 2MB build(which loads projects pretty fast). We were making bitmaptexts, sprite compression and custom builds with Phaser which you'd have kilobytes of projects. Of course, you'd do some of them with Unity too, but not reliable and you are not controlling it most of the time. Unity has tiny mode for the web but use cases are pretty limited as of now.
Yes, the tradeoff is different codebases, longer development but you'd have more opportunities, more reliable environment rather than depending on Unity, which is a blackbox.
Still, I'd try out some web builds on Unity to see how it goes. I don't know if it got any better. My thoughts are mostly from last year which may not be accurate anymore.