There wasn't anything the Republicans could do about slavery in the slave states, and trying to do anything about it would have split the country.
What Lincoln and the Republicans were concerned about was the spread of slavery -- and the break-up of the union. Giving guarantees to slaveowners in the slave states if it would preserve the union was an acceptable policy for them.
How was the federal government's presence felt in 1860? How did most people interact with it? The mails, the courts, the customhouses, maybe the land offices in the West.
Maintaining forts, delivering the mails, collecting import taxes were ways that the federal government could maintain that the union was intact, and work or wait to resolve the situation. So it's not surprising that the collection of import duties, like the delivery of the mails was mentioned in Lincoln's inaugural address.
The idea that "it was all about tariffs" was something that developed after the war when it was clear that support for "slaveowners' rights" wasn't an appealing issue to most people.
But if you really want to say that the Civil War was all about money and power that would apply to both sides. Don't pretend that there weren't strong economic motivations on the secessionist side that were even less legitimate than what you ascribe to Lincoln and the unionists.
Lincoln implied the use of force/violence in his address not over the ‘spread’ of slavery but amongst other things the collection of those ‘duties and imports’. Tariffs had been an issue with many of the Southern states for decades. South Carolina threatened succession in 1832 not over slavery but tariffs. Tariffs were a powder keg with the South. Slavery was the fuse. As it appears opinions are fairly set on this subject, I will peacefully ‘secede’ from further comment.