Zear... originally it did NOT... that's correct. However, over time, Sony released the Dual-Shock & the rest is history. Many upon MANY developers began adopting its support once that controller was released internationally.
Some games, like TWISTED METAL 2, released prior
to the Dual-Shock's release, etc. So, as you stated, many did NOT support the controller & then many from the late 90's did, etc.
Many AAA titles support analog use in one way or another for the ps1... whether it is just the left analog nub or both... say, for camera angle support or fighting games such as Tobal 2, etc. I recall Xenogears utilized both analog controls... for motion & also for camera angles, etc.
Also, let's not forget that the Dual Shock controller supports a rumble feature... hopefully a future firmware release for the Zero will begin to support, etc... if it doesn't already from the 8/20/14 update.
My main goal is just to purchase a PS Vita for that single purpose. I love the ps1 gaming era & if I'm not mistaken, the console has like over 1-2000 titles from ALL regions. Pretty impressive if you ask me.