Reaping what you (don't) sow.
The problems associated with downtime due to rebooting (and in this day and age only kernel updates should need a reboot) could be offset by a decent business continuity framework with dual servers.
Upgrade one while the other carries the load, and then switch and upgrade the other.
Of course that requires a finance department that accepts the "cost" of such redundancy is the "price" of permanent uptime. Which IME, they rarely do. Although they CAN tell you - to the penny - how much it's costing the firm when 1,000 employees can't do their job because downtime is needed to patch a server.