More and more airlines are using third party ground handling companies to handle check-in at outstation airports as opposed to their own staff (with the exception of the station manager who may be lurking nearby). Staff at these ground handling companies are assigned to different airlines (or group of airlines) based on which Departure Control System (DCS) they are trained on. In SQ's case, this would be Amadeus Altea Customer Management (also used by other airlines such as BR, LH, LX, AC and a many other airlines including those in other alliances).
The check-in desks tend to use Common Use Terminal Equipment (CUTE) where you can login to many different DCSs. Agents checking in Amadeus Altea DCS airlines would be logged in to Altea. They can handle check-in for flights on many different airlines that use the same system at the same time (only difference is that they would need to change the signage on the display for airline/class of service/ff status on the display monitor visible to the customers standing in line). As such, it would be a hassle to having to keep changing boarding pass and baggage tag stock (and updating the system to use a different print format etc.) when one or more counters switch over to handle the flights of another airlines.
In the past, some airlines would insist on using their own boarding pass and baggage tag stock. They would need to find space in either a storage locker or their own airline office to store these when not in use. After COVID, some airlines no longer have an airport office or may not even want to pay for additional storage.