Regarding the implimentation of the cards. I do actually think there is an issue and the majority of the players here are misdiagnosing it.
The problem is the meditation systems and the deck in the first place. The ability to change and shape the deck is rather symplistic, and the mechanism in play has higher RNG.
A better mechanism might be a more robust expansion of the deck building mechanic during the night times (AKA the segment the player has control over) paired with a change to the events themselves, where they draw hands 3 times, and then select based on best 2/3. This means lower probability of being screwed on something you planned for.
The deck building mechanic used to be a lot more complex. You had cards that boosted skills, cards that had special effects, etc. The player even picked and choose the cards to play, and the cards you didn't play stuck in your hand. So you had to plan what to keep for later, what to get rid of, etc. It was a fun system, but it didn't work in the context of the game. The more control you gain over the card system, the more it feels like you're in control of the Princess.
The current system as you see in game indeed pretty simple, but it's only the intro of the game. It has very simple cards because the game has enough complex ideas at the start without throwing you head first into complex cards too. The game is 55 weeks long and this version ends at 20, so you're just barely coming out of the intro as it currently ends.
First, skillchecks: it's a very classic approach: build up your stats to become better. Half of it works (the one where you built it up), the other half doesn't (where you use these skills in challenges). The problem is that the treshold of winning a skillcheck is (in most events) dependend on the time, meaning: being able to lift an axe requires 13 strength in week 5 and 30 strength in week 15, for the same axe. This is like the (very bad) idea of leveling up enemies when the player levels up; you completely lose the sense of progress and actually weaken the char instead of improving her.
I think I know why the developer did it, but I would argue strongly against it: if you want to have some kind of progress in the development of the princess, she should improve in what she does and what she is good at. If she can lift an axe in week 5 with 13 strength, she should be able to do the same in week 15. Your mechanics, as they are now, don't support this idea of improvement.
The checks in meetings with council members have to scale with time, because there's a variance of 12 weeks between when one could first appear and when it could last appear. If they all had static requirements, they would be impossible at the start, hard in the middle, and a breeze at the end. This would indeed give a sense of skill progression, but skills are not the things you are progressing in this game. It's the relationships with the other characters. If they were all static, which characters the Princess could build goof relationships with would be essentially randomized, the ones at the start would be impossible.
It's very true that at the end of the run the player should be able to look back at the past events and say "Wow, look how much I've grown and changed". But you're misinterpreting where that growth is. At the end of the game (the whole game, not the current version) the player isn't supposed to feel "The Princess is so much better at conversation now!", they're supposed to feel "Wow, Gales hated the Princess's guts and now they're BFFs!"
Second, cards: a very bad mechanic as of now. There is no progress in this card game whatsoever, you keep the same deck that you built in the first few weeks. It's a static mechanic where the player can tweak the possibilities for card draws, and once you know what you want you keep the deck and hope for the best.
You can in theory get 5 of each color and cause it a day, but you'd do very badly. You want to be micromanaging the deck much more closely as there are checks you'll want the Princess to fail at if you want specific outcomes. And pushing your odds up for an important decision and then taking those cards away is a pretty good strategy. Even if you do have your deck "perfect" and never want to touch it ever again, as the game goes along as there are events which add cards which change the odds. For example, the Vizier adds pink cards to the deck pretty often if the Princess isn't going along with everything he says. So if the Vizier is your trainer but you don't want his ending, you'll need to fairly constantly re-balance things to remove the pink cards for other stuff.
One of the big problems I see is that the card draws have a high impact on story line and story progression: take, as an example, the relationship between princess and brother. Whether they are on good or bad terms is dependend on one random card draw. It's not dependend on their relationship up to this point, nor on something like their general personalities or whether they like or hate each other, no: it depends on whether the princess draws yellow or not.
This I agree with, which is part of some changes coming in .31. Card checks determining major plot points is problematic. Things like which trainer you end up with are major game altering decisions that can't really be recovered from. For the most part, failing checks is something you can overcome over time or actively want for your goal, but kicking out Cecily when you want to play her route is just bad. So anything that hinges on one check like that needs to be changed. For Cecily I'm adding the same system you have with the Vizier, where you can force the Princess to change her decision at the cost of stat penalties. The other one that needs to change is the brother check early on, as that has some fairly pervasive consequences and is actually completely random.
Once again this contradicts the basic premise of the game ("pushing the princess in the right direction") because the princess has no starting point / personality. It's random whether she like her brother or not, whether she gives asylum to refugees, whether she flashes her tits to Ulric or not; there is no element of corruption here. All you do is built up your deck in the first 5 or 6 weeks and then hope for some good rolls.
First of all, I've never said this game is about corruption, like ever. Everyone thinks it is, but it's not in the blurb or anything. That stuff is there if that's what you want, but there's a lot of endings in this game that will require you not to corrupt the Princess at all. Specifically the endings where the Princess romances council members won't trigger if she's corrupted by her trainer or the player. Secondly, there's an entire mechanic that you've missed largely because it's not very important at the start. When you talk to the Princess, as well as adding a card to the deck and boosting skills of a certain color that week, you effect your relationship stats with her. That you missed this is largely bad interface design as these numbers were hidden away on the people screen. But balancing these states is very important as the game goes on because letting certain things get too high/low can have pretty bad consequences. And if you want to corrupt the Princess, get her reliance really high. To get to the PC corrupting the Princess endings (which obviously aren't in the first 20 weeks), you want to get her Reliance very high, get her Love up moderately high, and make sure none of the other trainers have corrupted her themselves.
And oh, look at that! Doing do has tension with getting better at skills and manipulating the deck because you might have to pick options that don't match the color you need right now. Wow. it's almost like I've thought about this system.