Crosscourt training improves consistency under pressure, increases accuracy by forcing aiming at half the court, and enhances defensive skills by requiring players to deal with a high volume of balls from the back.
This overview of coach Ewan's tournament training session with his friend Jake is quite insightful. It gives you a look at specific drills they use, like the basket drill combining volleys and overheads. Ewan explains the benefits of playing crosscourt games for improving consistency and defense. It's useful to see how players at a higher level structure their practice and think about strategy on court.