I am with you on this, somewhat. For Counterfeit, I see nothing wrong with the playing of a Duration multiple times extending to the final resolution of the longest lasting Duration play. In that case, the Counterfeit itself stays in play, and trashes the card when the Duration effect ends. Think of it as a Throne Room (for Treasures) with added instructions to be done once the throning is completed. Rebuild could also work in this way.
Throne Rooms already work that way, and Counterfeit is indeed a Throne Room. The card text would have to be changed to specifically address Durations though, somehow saying that the trashing happens after any future effects. Sounds messy. The only alternative I can think of is "the next time you discard that Treasure from play, trash it." Not exactly better than the current fix.
You have missed my point. Counterfeit reads "... you may play a Treasure from your hand twice. If you do, trash that Treasure". So what is it to play a card? Is it putting it into play and resolving it for that turn? Or is it fulfilling all of the instructions on the card (which requires multiple turns for Durations)?
It appears that the first interpretation is being used for Durations, which means that a Treasure-Duration is to be trashed during the Buy phase of the turn that it is put into play. The loss of the card before its Duration effect is done is what is causing problems.
What I am calling for is to change the interpretation of playing a Duration to saying that the playing of the Duration is not done until all of its instructions are completed. No change to the wording of Counterfeit is needed in this case. Instead, if you have used Counterfeit on an Astrolabe, you get $2 and +2 Buy now, $2 and +2 Buy at the start of the next turn, and then (as part of the start of the next turn) trash the Astrolabe. (I would wait until the Buy phase of the following turn to do the actual trashing for tracking purposes. This also leads me to wonder if a Treasure-Duration should read "now and at the start of the Buy phase of your next turn".) As with Throne Room, the Counterfeit would stay in play to track the Duration being played twice and to also track the fact that the card is to be trashed once it has become fully played.
This change would also help with Procession (as it was originally worded). The trashing of the Duration and the obtaining of a more valuable card would wait until the Duration was fully played.
There are several problems with this suggestion.
We resolve an ability by following each instruction in order from top to bottom. Some instructions tell us to do something later; these set up future effects. Your suggestion entails stopping after such an instruction and not continuing resolving the ability until all the future effects are resolved. Throne Room has two instructions: Play a an Action card from your hand, and play it again. (These are two separate effects that happen after each other.)
Let's take a non-Duration card, Merchant. If we Throne Room Merchant, we play it once, getting +1 Action and +1 Card, and setting up a future effect when Silver is played for the first time later. But that future effect hasn't happened yet, so we are not done playing Merchant. That means we don't continue to the next instruction on Throne Room yet. When we play a Silver, Merchant is done, so now we play it again, getting +1 Action and +1 Card, and failing to set up a future effect (since the first Silver has already been played). Obviously this is not how Merchant should work.
Maybe your idea was that this would be a special rule for Durations, but the problem is the same. If we Counterfeit Astrolabe, we only play Astrolabe once this turn, because we're not done playing it the first time until the start of our next turn. At that point, after getting +$1 and +1 Buy for the next-turn effect, we play it again, getting +$1 and +1 Buy and setting up an effect for
next turn, making Counterfeit and Astrolabe stay in play one turn more. At the beginning of
that turn, after getting the next-turn effect again, we trash the Astrolabe.
What if we play Conclave on Wharf? Since Wharf is not done being played until the beginning of next turn, that's when we get the +1 Action from Conclave. But Conclave doesn't even stay in play to remind us of this.