As of the latest information (2021), all seats on Japan's Shinkansen (bullet trains) require advance reservation and have assigned seat numbers. There are no unreserved (non-reserved) cars on most Shinkansen services, including the Tokaido line between Osaka and Tokyo.
Some slower services (e.g., certain Kodama trains) may have non-reserved cars, but the primary Nozomi, Hikari, and Sakura services are fully reserved. Always confirm at booking.
Cost for a reserved seat Osaka–Tokyo (Tokaido Shinkansen) is approximately ¥14,500–¥15,000 one-way in ordinary class.