I think this is correct - because that is one big area where TCP and HTTP really fall short.

HTTP/2 should be a huge improvement for lowering latency in anything but the simplest web sites, without having to use ugly hacks such as sprite sheets and putting all your javascript/CSS in one file (which is sub-optimal in terms of caching if you want to update say a single javascript file, because then a user with a full cache has to re-download the huge concatenated javascript file instead of just the single source that changed), and avoiding spanning things across multiple domains to get around browsers having a connection limit.

Doing many requests over the same connection is very common.

right. The other key fact is that request header compression is necessary to make parallelism work when interacting with tcp congestion control. Its critical.