The browser's html engine will still do conditional jumps based on the HTML. One attack [1]:
"Decompressors, especially in HTTP(S) stacks. Data decompression inherently involves a large number of steps of "look up X in a table to get the length of a symbol, then adjust pointers and perform more memory accesses" — exactly the sort of behaviour which can leak information via cache side channels if a branch mispredict results in X being speculatively looked up in the wrong table. Add attacker-controlled inputs to HTTP stacks and the fact that services speaking HTTP are often required to perform request authentication and/or include TLS stacks, and you have all the conditions needed for sensitive information to be leaked."
[1] http://www.daemonology.net/blog/2018-01-17-some-thoughts-on-...