As a very rough approximation, I suspect that html parsing (beyond the streaming of the data anyhow) isn't really all that fundamentally serial. After all, if you seek into an html document at some random point, you can generally interpret the html structure mostly locally, i.e. it's likely possible to subdivide the task of parsing an html document.

Given how leniently html deals with errors and that some of the parsing rules have some context sensitivity (the various modes) actually exploiting large-scale parallelism is probably a very difficult bit of engineering. Additionally, there may be corner cases that have much more context dependence than normal. Also, parsing is already probably not a huge part of a browsers runtime, and aggressive parallelism might be faster but more power hungry for a very small latency win. But I can't think of a specific fundamental limitation that prevents the normal parsing case from being quite parallelizable; I believe it's "just" an engineering problem.