i use animate for all the ios and android apps and games i've been contracted to create. i use animate for some (eg, those with a lot graphic animations) web pages that use html5/canvas. but for most html5 webpages i use jquery, css, html and a text editor. (my favorite for the past few years has been sublime text.)
but i haven't been asked and i haven't done any swf web sites/pages in the past few years.
as far as dreamweaver (dw) is concerned, i tried to use it many (when macromedia owned flash) years ago and found it difficult to get it to do exactly what i wanted. i guessed it would take me about the same amount of time to master dw as it would to learn html. (i don't think css was even on the horizon - it certainly wan't on my horizon at that time.) i ended up with a text editor which allowed the pixel perfect control i wanted and i learned html coding. and i've never been tempted to return to dreamweaver or any other wysiwyg program that, is supposed to, streamline the process of html creation and have since added css, javascript and jquery to my toolbox.