You mean:
Campaign/Campaign Ops
Nyzul Assault
Assault
Ashu`Talif Assaults
Limbus
Einherjar
Abyssea
BCNM/KSNM/KCNM/HCNM/ENM/ANNM/ISNM (only limit beyond time is how many seals/points you have)
Dynamis (daily event now btw.)
Voidwatcher
Before people got butthurt over level caps it was existent in almost all CoP areas, but time limits existed in almost every event the game has to offer.
Also, no. Most of FFXI's quests didn't have cutscenes on the scale of mission cutscenes, only a select few did. However they did have a type of cutscene that just threw instanced NPCs into the areas to further the story, but it wasn't exactly a cutscene in terms of what you'd get with missions, or like:
http://www.youtube.com/watch?v=XAdox...eature=related
So before you call others liar...at least be clear yourself.