To be honest, I hate the idea of there being any sort of time limit in an adventure game. The beauty of adventure games is being able to relax once in a while, not having to constantly shoot something, run from something, perform leaps and jumps, hide from something, dodge something, or perform some other action associated with quick fingers and reactions. That's what I've loved about adventure games - it's a time when you're giving your reflexes a rest, and instead letting your brain and creative mind take over while you get immersed in a unique and interesting world. Unfortunately, a time limit (no matter how drawn-out it may be) can do nothing but damage that relaxing, laid-back experience that comes with playing an adventure game. It would require the player to do everything quickly, and it would make them feel like they have to rush the thing; something which the adventure game genre simply should not make a player do, in my opinion.
Subsequently, a time limit would ruin almost everything that's great about an adventure game. It would discourage exploration and experimentation, for one thing. Whenever I've played adventure games, from a young age until now, I've always enjoyed exploring every nook and cranny of the environment, and have had fun with trying out random, illogical item combinations purely to see what the character response(s) would be. If I were to have a time limit throughout the entirety of my playtime, it would discourage me from experimenting with and exploring the virtual world around me; I'd be more inclined to simply search for the solution straight away. As a result, I'd probably miss out on a lot of content, and would ultimately be deprived of a lot of the depth within the game and the potential enjoyment that it may hold.
In fact, this is precisely what happened to me when I played the first level of 'Space Quest 1' (which I only played recently). See, with the 'King's Quest' games, I'd like to do the aforementioned and 'look at', 'examine', 'pick up', 'talk to' almost every single bit and piece of the environment. Why? Because a lot of the subsequent responses were often quite funny or interesting. I was looking forward to doing the same thing in 'SQ1'. However, the first thing that I was presented with upon playing was a lovely, big countdown clock in the corner of my screen. This prevented me from going about my usual adventure-gaming routine, which I instead had to exchange for a more rushed and fast-paced approach. Ultimately I was given a less enjoyable experience; the time limit detracted from the whole experience that the first level could have held. I actually felt cheated, to be honest - cheated out of an enjoyable section of the game - to the point where I'd gotten rather pissed off and decided to resort to a walkthrough (something I very, very rarely do). So, to have an entire adventure game be based around a time limit would just suck, for me, and would probably turn the game into something unenjoyable.