When it comes to quests with time limits, you won't be able to miss scenes, because failing to complete a quest within the time limit will result in a game over. All quests with time limits will have to be completed in order to progress, at least with how the game is currently structured.
I had to read through this a couple of times to figure out what you were saying, because the whole paragraph (after the first interrogative sentence) is one long run-on sentence.
You say that, for you personally, a time limit is unnecessary and doesn't make the game more fun, and so you don't find my point valid. You seem to be missing the point entirely. The time limit isn't necessary in order to make the game more fun. The time limit is necessary because the story has to be completed in a set number of days. And this isn't something which you would have to read through thousands of posts in this thread to find out. The game itself clearly explains this.
The game tells us that the MC's participation in the show will last for 140 days, unless she gets disqualified. That right there tells us the total time limit for the game, once the show starts. The managers, when they meet with the MC, tell her that she will have to complete a minimum of 15 tasks. So the MC has 140 days to complete 15 tasks, probably one at a time. So of course every task has to have a time limit, otherwise the game would run over the 140 days.
This has nothing to do with whether the time limit makes the game more or less fun for you. This has to do with the story which the developers are telling. In their story, there must be a time limit.