I can appreciate why it was cool. "What if everything could automatically do the right thing when it interacts with other things, and you wouldn't need any of this ritual boilerplate stuff? Why do we keep needing to convert from string to number to string over and over and over it's crazy. The language should just do the right thing!"
I think it's very easy to be sympathetic to the design trend.
Then there is the fact that PHP and JavaScript were basically domain specific languages at their inception.
PHP was a hypertext pre-processor. Pearl, but stripped down for templating.
JavaScript was an alternative to Java applets. When you don't need the full power of Java, you could throw in a few small scripts.
To make things a bit less intimidating, the weak typing seemed like a good idea, and for these use-cases it might very well have been. If you don't know how to program and only want to display some fancy styled text, why would you need to understand that a number isn't a string?
But there was the pattern, that "real" programming languages like Java and C/C++ were hard to learn for the average "creator", so they took JS and PHP as entry and built up their skills from there, building bigger and bigger solutions with those tools.
I think it's very easy to be sympathetic to the design trend.