That's always been the plan. Even in the original 2016 presentation featuring the considerably larger Interplanetary Transport System that got scaled down to become what's now known as Starship and Superheavy, the plan was to churn them out en masse to make it possible to make the most of each Earth-Mars transit window.
Starships and all the parts that comprise them are designed to be mass produced and treated as cattle rather than pets.
Their own deliveries of fuel and client payloads will be delayed from the airspace and downrange surface exclusion zones.
Once you've got vehicles in space you'll need 24/7 monitoring and management. Even if mission control teams are relatively small the only way you'll be able to safely manage a large number of missions will be with a large number of teams.
The personnel and infrastructure costs will put a cap on the number of Starship launches SpaceX will ever be able to manage. The costs of those will push up the costs beyond Musk's low-ball fantasy promises.
But that doesn't matter. Even without any Starship re-usability (aside from Superheavy), you still come out far, far ahead of any conceivable evolution of SLS.
1. None of the current public Starship designs include payload doors. So none of these are in any way useful as launch vehicles for orbital payloads. Payload doors a huge structural weakness and requires a lot of engineering effort. None of the current public Starship designs have an obvious "payload doors go here". A Starship-based delivery vehicle will likely be a separate design from the manned vehicle.
2. In-orbit refueling is not just an unsolved problem it's a largely unexplored problem. Moving fuel between two vehicles in free-fall is going to be a monumental challenge. You'll basically be running the same pump mechanisms you'd use for the rocket motors but feeding into a flexible umbilical between vehicles. Starships are huge so you're talking about docking two huge vehicles (one of which is nearly empty of fuel for maneuvers), connecting an umbilical between them, pumping fuel through the umbilical (in free-fall), then undocking and the two go their merry ways. None of that has been done and involves hundreds of individual challenges.
3. Musk (not necessarily SpaceX engineers) is making grand promises about the turn around time for Starships. I think they're wildly unrealistic. A large vehicle undergoing a lot of extreme dynamic forces in a flight is going to need a lot of examination before it can be safely relaunched. SpaceX is likely going to need to construct hundreds of Starships to maintain anywhere close to the promised cadence of launches. The manpower to refit vehicles is going to be expensive. There's a big difference between reusing a booster core and a vehicle that had to survive orbital reentry.
4. Even if launch costs were hundreds of dollars per kilogram it doesn't make any other aspects of spaceflight less challenging. If you send people somewhere they need their vehicle and life support launched with them. A broken toilet can still kill the crew. Just because it was cheaper to launch doesn't mean you get to scrimp on other expenses. The Space Shuttle was expensive not because of the marginal cost of the launch itself but the operations/personnel costs of the Shuttle program.