I've only done PHP for small personal projects and some wordpress hacking, and that was years - so my experience is limited. But it seems to me that one of the great and tragic things to PHP is the low barrier to entry. As you put it: "first open source language in which just anybody could write server-side web applications without terrible management problems for the sysadmin".
This made it extremely easy for anyone in the early 2000s who signed up for a web hosting account on godaddy/hostmonster/hostgater/etc... to fire up a text editor of their choice and start slinging code and FTP'ing up to a server. Didn't have to worry about installing, configuring, all the dependencies, build tools, etc... just edit, upload, refresh -- lather, rinse, repeat until it works. Lowered the barrier to entry, and got a lot of people into the field. Really powerful stuff.
It also made sloppy, hacked-together, copy-pasta code very prevalent. In my limited perspective, I suspect that this prevalence of sloppy spaghetti-code has contributed to PHP's bad reputation. It's not that you can't do good code (totally can!), but a PHP environment can be forgiving of some pretty bad practices.
PHP has a low barrier to entry, but that's a great thing in my opinion. It's something that should be celebrated, and at the very least, it shouldn't be a criticism!
Bad developers exist in every language, and no language is completely wart-free. People just like to zero in on PHP to criticise it because it's easy, and it bugs me a bit (especially if they're simultaneously singing the praises of another less than perfect language such as JS or Python or Go).
At that time you could have made similar software for JSP, ColdFusion or ASP.NET but hosting would have been much more expensive and a big hassle. With PHP it was feasible to offer a $5 a month hosting plan good enough for blogs and simple web application.
I wrote a lot of PHP because it was a great way to deliver products to customers, particularly ones that didn't have a lot of resources for "ops" but also a place where I could write open source software which might really get used and have an impact.