I love Smalltalk, but it has some problems with it that are solved by the web browser.
Firstly, Smalltalk is a computing environment built around the concept of Personal Computing. You can open up and redefine the functionality of anything running on the system. This obviously makes it very prone to abuse. It was a system that was not built on the principles of running any random source code coming from a foreign party. The focus of the system was to elevate the concept of computing for the individual.
The web browser, on the other hand, has been built from the ground up on the principle that it would be running foreign and inherently untrustworthy code.
The web browser is approaching what Smalltalk was aiming for, however, with a focus on running code in a secure, sand-boxed environment. I don't feel like this is an inherently conscious trajectory but the fact that JavaScript has significant influences from Smalltalk-80 has probably helped to guide this path.
The advancements in networking and multimedia present in HTML5 are allowing for this sandboxed and restricted environment to more fully express it's influences from the Smalltalk systems.
Secondly, the open nature of the web browser and it's standards have encouraged adoption whereas the closed and proprietary nature of Smalltalk systems played a large role in it's "failure".
Designing by committee and standardization has it's pros and cons, but ultimately it promotes adoption and helps a system to survive in the overall ecosystem of computing systems.
I don't blame the web for the death of such amazing computing platforms as Smalltalk and Lisp machines, I blame market mechanics.
Microsoft succeeded with it's approach to Personal Computing because it focused on what the customers demanded for their short-term business goals, rather than some enlightened ethos of enabling humanity through better tooling. These corporate customers actually benefited from the opposite. Lack of control over a computing environment was seen as beneficial to the overall goals of the organization and is the antithesis of the goals of Smalltalk.