Most leases have a clause governing assignment and subletting. When you add or replace roommates you are subletting part of the unit, so the subletting cause in your lease applies.
If you’re a sub-tenant/not on the lease, what are your rights? Can the master tenant kick you out, or raise the rent, at his/her discretion?
It doesn’t make sense to give the landlord a say in picking your roommate. The original tenant or tenants are still responsible for paying the rent.
Why do you need the landlord’s consent? Because it says so in the lease and you will be in breach of the lease if you don’t get his consent.
The truly bad master tenant collects all of the roommates’ rent and then, for whatever reason, doesn’t pay the landlord. Usually you find out about the problem too late, when you’re being evicted.