You send drawing 1 to player B. They watch it being drawn and guess. They send you drawing 2. When you open your app you see drawing 1 happen again and player B making their guess. You can skip that. Then you're shown drawing 2 and can make your guess.
You can "pass" during drawing 2, but that ends the game (streak) between you and player 2.
And though the streak doesn't really matter, it means that, no, you can't really 'skip' watching the other player's drawing stroke-by-stroke. You can only choose to stop playing.
I think they hit the right compromise here. As you said you can give up and pass on the word. If you get the word early then it shows you the final drawing then moves on to the next turn.
Not allowing someone to skip to the final drawing when they do want to play but can't guess the answer yet is a feature, not a bug. It allows new strategies, like drawing a series of states to show a change. It also gives you a sense of the other person, it's a big part of the fun sense of communication that you get with the game.
A skip button, if added, would be widely used and make the game worse.
There actually is a "skip watching" button, but it is white on white until the other player colors into that corner. I believe it is in the top left corner.
Sometimes you actually need to watch the entire thing to get it. As in, your word involves some change over time that you want to portray with multiple pages.
You can "pass" during drawing 2, but that ends the game (streak) between you and player 2.
And though the streak doesn't really matter, it means that, no, you can't really 'skip' watching the other player's drawing stroke-by-stroke. You can only choose to stop playing.