One major argument is that the slaves could have been bought at a lower cost than the war.
Even today, that argument continues.
The basic math is that the war cost the north about $3.4 billion in 1860 dollars. Add in the cost to the South and it goes beyond $6 billion.
https://www.princeton.edu/rpds/papers/Golding_Lewis_Economic_Cost_of_American_Civil_War_JEH1975.pdf
There were roughly 4 million slaves at the time and the average price across gender and age in 1860 was roughly $800. Multiply the two and the cost to buy all the slaves is roughly $3.2 billion.
Anyone could argue those numbers are off a few billion dollars but if you add in the human suffering and loss of life, it would have been a much better solution.
Lincoln did make all sorts of offers and proposals to buy slaves rather than emancipate them for free but A) it was too late as the war started before he took office and B) no offers by slave owners were accepted.
There are a two major counter arguments as to why this didn't work: 1) Slavery was good and is worth fighting for - yes sadly, that was the main argument believed by the Confederates. Their most eloquent leaders on this principle were called The Fire Eaters and they wrote a lot on this topic and were very influential in moving the Southerners to chose war over Union. Thus, the war wasn't a rational financial decision where we can look at the math and say that makes better sense. 2) Economics - trying to buy up all of a product from millions of different owners isn't going to work. The law of supply and demand will allow owners to continue to raise prices. Plus, it was a massive cost to agree to up front with little public support to pay for it