Did it? Web applications are not inherently more (or less) stable than native applications, and OS compatibility issues were replaced with browser compatibility issues.
Absolutely. The browsers are extremely stable and generally don't crash. The individual applications may still be bug prone but those bugs generally don't take down the system.
> OS compatibility issues were replaced with browser compatibility issues
Sure, but it's a much less severe problem (the potential for bugs rather than binary incompatibility) and one that developers can easily remedy based on visitor statistics without customer's having to download, update or take any action. This problem also becomes much less of a problem every day as the browsers converge on common standards.
Only Firefox and Chromium are able to keep up. It's an improvement over native apps working only on Mac OS and Windows as they are mostly open source, but still only two platforms.
The killer feature is effective per-app sandboxing.
The eventual advent of the iPhone and the subsequent explosion of the app store also demonstrates that ease of entry is unimportant. The iOS platform was and still is the public platform with the highest barrier to entry, yet none of that matters because getting secure software distributed easily to users is the ultimate killer feature.