Basically, Sega's strategy after Dreamcast era was to focus on exclusives, although there were few exceptions (NBA 2K, Phantasy Star, Worms 3D were multi). They decided to port and create games on specific platforms according three factors:
customer profile, hardware profile and console manufacturers partnerships.
Gamecube got the Sega's games able to target a friendly large (kid) audience and needing to reproduce levels of vibrant colors: Sonic Adventure 1&2, Super Monkey Ball, Billy Hatcher, Skies of Arcadia, Virtua Striker 3, Beach Spikers. And F-Zero GX following a hardware partnership with Nintendo.
PS2 got the teenager/adult edgy games: Head Hunter, Yakuza, Virtua Fighter 4, F355 Challenge, REZ, Virtua Tennis 2, Initial D...
Xbox got the Sega's most ambitious projects since it was by far the most powerful machine on the market: Panzer Dragoon, Outrun 2, Otogi, JSRF, Crazy Taxy, Gunvalkryie, House of the dead 3 and Shenmue 2. The power of Xbox hardware was preeminent in the Sega's agreement with Microsoft on the Shenmue 2 deal, although it may sound surprising since Shenmue 2 on Xbox looks a really lazy port.
All that plan was established at the time that PS2 had yet to get a fair amount of libraries. Needless to say, Sony's console was too weak to inherit these games from Sega. They could have decided to port these games afterwards on PS2 but the initial sales were disappointing. Sammy came over to own the company and it was the end of the strategy.