No, that is surprising, there is nothing inherently CPU intensive to run an email client, it should be almost free, even inside an emulator.

People are making impressive 64k demos on the web these days.

Demoscene is spending a lot of effort to make things as efficient as possible. Other programmers have other priorities. Clearly the performance is what it is because "running in a browser" was deemed non-negotiable (as it strengthens Google, and then the performance just had to be "good enough" (with Google's lead and market size).