Personally I've never liked tying downtime training to leveling. I assume people are "training" all the time. A fighter may have learned a new technique and simply doesn't use it until they're comfortable with it. In order to get comfortable the new technique becomes part of their nightly exercises. A wizard studies continue even on the road.
I know that when I'm learning something new as a software developer, it takes both study and application before I feel like I've actually gotten better. It's kind of foreign to me to think that my skills could not improve incrementally simply because I haven't had a class or taken a week off just to study. In fact, that week of study could easily just be the starting point of mastering a new technology.
In other words, D&D isn't particularly granular. New skills don't just happen overnight, it's a gradual improvement. Gaining concrete levels is used for simplicity, but people are incrementally getting better all the time.