Cloud is successful with Pay-per-use model in software, because it invented elasticity. The most important point about elasticity is that - 9 machines that are serving a company during the day time will shrink to 1 machine in the night automatically based on load. The 8 machines that are released will then start serving the other company along with 1 other machine. This property of cloud that allows 2 tenants (or more) to share processing capacity is called shared-process multitenancy.
So why not stateful architecture?
Lets just say 1000 users are distributed across these 10 machines during day time i.e. 100 users in each machine. In a stateful architecture, the 100 users will be served only the server that created the session for the users during login. This happens because the session state is stored in the memory of that server. This is done by the http load balancer and is called session stickiness.
When night falls, lets assume that 900 users are logging out of the system, while the rest of the users (i.e. 100 users) are still logged in. Ideally, 1 machine should be good enough to serve all of them. However, these users could be distributed across all the 10 servers with 10 users each. So shrinking back to 1 machine is not possible i.e. it breaks elasticity.