The latter proposal is just punting on the problem of what math to teach when. You're going to teach some subset of math first. You might disagree with the particular ordering that is mainstream now, but calling it 'year 1' and 'year 2' just begs the question. Yes, focus on problem solving is good. Yes, these problems are dumb. But people still are going to learn what a cosine is sooner or later, and you have to decide when, and you're probably going to put in the course description that yeah, you learn what a cosine is this year.