The question of Flash is to some degree a political and personal one. Until the arrival of iOS, almost all Internet browsing devices had Flash installed, ie, websites could assume that Flash was available. Smart phones and tablets changed that; starting with iOS which didn't allow the installation of Flash, a small but rapidly growing subset of the web browsing public did not have Flash. This kick-started (or gave a big boost) to efforts to incorporate the playing of video into the next version of the HTML spec, HTML 5 (and thus into the browsers directly). Android had Flash for several years but in 2012, Adobe threw in the towel on this one (it didn't run too well on the comparably low performance mobile CPUs).
Nowadays, a lot of (most?) websites offer HTML 5 video streams that play without Flash, Youtube included. Not installing Flash is clear signal to the websites that one wants an alternative, ie, something built into the HTML spec not requiring a plugin. This will thus accelerate the demise of Flash. For some that is a good reason to not install it, to others the urge to kick out Flash is not that strong. Not installing it or installing something like Click-to-Flash, which blocks the Flash animation until one clicks on a placeholder served instead of the Flash content, brings other benefits of, initially, less animations and popups and often thus less ads, less CPU usage and longer battery life, until all ads also have an alternative version to Flash. Additionally, since Flash had a good share of vulnerabilities, one removes one attack vector. Which applies to other plugins as well, like Java.
To have a solution for those websites that still require flash to fully function some people have Chrome installed, which has its own version of Flash included into the browser, maintained and updated by Google, to use on those sites.
With Safari, my experience is that a lot of websites serve video as HTML 5 even though I have Flash installed. This might be Safari asking the websites for this explicitly.
