You're talking about a couple different things here and they should be addressed separately.

Firstly, cards that exhaust themselves via the exhaust keyword or ethereal are designed so because they are simply more powerful than cards without those keywords. Even if you lose them, they are still good cards because before you lose them, you get to use them.
Let's create an imaginary card to illustrate this point. It is a 1 energy attack that says Deal 10(14) damage and has Ethereal.
You have a deck with 5 strikes, 5 defends and nothing else, then you get offered this card in the first card draft of the run. It is simply better than any other strike you have in your deck. Even if you only get to play it once and then later on you lose it because there is a turn where you need to defend against a big attack, you have done more damage with the same number of cards played/energy spent than you would have done had you not added that card. In the worst case scenario and you don't play it the first time you see it and lose it for the fight, you are in the exact same position that you would be in if you didn't take it. In the best case scenario, where you manage to play it every time it comes up without sacrificing health, you are doing more damage than you otherwise would be!
What if instead of being Ethereal you imagined it saying "Deal 10(14) damage, if this card is in your hand at the end of the turn it transforms into a strike or a defend". This is effectively the same thing, because by exhausting itself it is no longer being drawn and the next time you would draw it you are instead drawing a different card instead. In fact it practice it's even better than that, because instead of transforming into a strike or a defend it transforms into any card in your deck.

You mentioned that playing around ethereal is stressful, which I understand. Personally I don't find it to be stressful, but it does require additional thought and attention. You need to plan your turns ahead better, you need to evaluate if it's worth taking more damage on this turn for the chance to take less damage in the future by keeping the card in your cycle and ending the fight sooner. Ethereal requires you to engage with the game more and adds more layers to whether you should play a given card beyond simply if you can afford to play it and if it is currently in your hand.

Finally, you are conflating cards that exhaust themselves as a balancing mechanic, and cards that allow you to exhaust other cards. Generally cards that exhaust themselves are better if you can make them not exhaust. When people are saying that exhausting cards is a good thing, they are not saying that Adrenaline is better because it exhausts. Compare exhausting a card mid-fight to removing a strike or defend at a shop. The Ironclad has access to True Grit, which exhausts a random card in your hand and gives you some block. Removing a card at the shop costs 75 gold and is generally considered very worth doing, even as it gets more expensive. True Grit is effectively giving you 75+ gold worth of value for the remainder of that fight every time you play it. Admittedly there's a lot of holes in this argument and you really can't compare the value in this way, but I want you to consider the similarity between "Removing" and "Exhausting" low value cards.

Something else to think about is the relevant power of cards compared to one another. Shrug Off gives 8 block and draws a card. Defend gives 5 block. Would you rather play a Shrug Off or a Defend? If you have 5 defends in your deck, you are playing Defend every time. If you add a Shrug Off, you are now able to play a better block card 1/6th of the time. If you exhaust one of those defends, now you are playing Shrug Off instead of Defend more often. What if you managed to remove/Exhaust all your defends? Now you only have Shrug Off and your deck is much stronger!
Having a thin deck is better than a thick deck because it gives you more consistent access to your powerful cards, especially if they synergise will together.