In truth, the fundamental capabilities of the modern web platform matches and typically exceeds anything that was offered by Flash. What these people are really lamenting is the ease of authorship that Flash provided to non-technical users.
Macromedia/Adobe provided a suite of powerful tools for authoring Flash animations and applications. There is no free equivalent available targeting HTML/JS. This is not a problem of capability in the platform technologies. It is because there is no economic incentive to make and give away such tools. What equivalents do exist in this sector cost money.
When it comes to Flash, the old adage, "if you're not paying for the product, you are the product" holds true. The Flash authorship tools were free because 3rd party authors creating Flash content were assisting in the promulgation of a proprietary platform that was gradually replacing open web standards. Had they succeeded, Macromedia/Adobe would inevitably have looked to squeeze and monetise their domination of the web.
Programmers are often accused of not understanding what Flash offered to artists. Maybe that's true, but I've not encountered many artists who conversely understand the above.