I'm not sure I see the use-case there as being more useful than JS based WebSockets. Writing a general JS library to do what you suggest would be pretty straightforward, and the server-side work wouldn't be any different (serving partial HTML based on request type).
If your users are worried about security / performance enough to turn off JavaScript, they probably wouldn't want "HTMLSockets" enabled, either.
If your users are browsing with a browser so old it doesn't have a reasonable JavaScript engine, then it wouldn't support "HTMLSockets," either.
Basically, there's nothing you could do with "HTMLSockets" that you can't do with WebSockets, and with only a small layer to make it so. However, there's a whole host of utility that you get from WebSockets that you could never get from HTMLSockets, or would require a huge amount of hacking in order to get it to work.
And all this is beside the "pureness" argument, where one might say that HTML is for data, CSS is for design, JavaScript is for behavior; WebSockets are behavior, not data.
This is like asking why we should bother having any (new?) HTML or CSS standards at all, when you could write a custom rendering engine in JavaScript for every website.
There is tremendous value in having a solid, usable foundation for web development that doesn't rely on an imperative language to work. To start with, declarative features are semantic and allow for semantic upgrades on wide-scale basis. Do you like your Firefox/Chrome spell-checking in text areas? Do you like them being resizable? Well, this wouldn't be possible if all textareas were some JavaScript hack. (Hey, with only small layer you could actually fake a textarea. Does that seem like a good idea in retrospect, though?)
Also, it would be great to be able to develop simple dynamic web applications (or prototypes) without doing something complex. Progressive enhancement is buried far too early.
If your users are worried about security / performance enough to turn off JavaScript, they probably wouldn't want "HTMLSockets" enabled, either.
I frequently browse with JavaScript blocked by default, and I can tell you right here that this assumption is invalid. There is a world of difference between JavaScript library and a standard, declarative technology. The latter is more likely to be faster, have less bugs, no side-effects and be secure.
If your users are worried about security / performance enough to turn off JavaScript, they probably wouldn't want "HTMLSockets" enabled, either.
If your users are browsing with a browser so old it doesn't have a reasonable JavaScript engine, then it wouldn't support "HTMLSockets," either.
Basically, there's nothing you could do with "HTMLSockets" that you can't do with WebSockets, and with only a small layer to make it so. However, there's a whole host of utility that you get from WebSockets that you could never get from HTMLSockets, or would require a huge amount of hacking in order to get it to work.
And all this is beside the "pureness" argument, where one might say that HTML is for data, CSS is for design, JavaScript is for behavior; WebSockets are behavior, not data.