It isn't really a cost/problem to "ask the whole population to replace their coins". Coins are constantly being circulated, with worn ones replaced by new ones anyway.
The cost of changing comes primarily from businesses having to update vending machines, coin counting machines, etc (as well as increased production costs due to the new security features.)
But this switch has been planned for many years, so businesses have had a long time to prepare.
From experience, the lighter weight makes the coins harder to tell apart. The old coins had three denominations: 1kr (~$0.10), medium sized, thin, silver; 5 kr (~$0.5), big, thin, silver; and 10 kr, small, thick, golden. Their big size (compared to Euro coins) make them comfortable in the hands and trivial to count the right amount.
By comparison, the new, smaller coins are much harder to grasp and the new denomination (2kr) is hard to tell apart from the new (1kr). The new notes are similarly hard to tell apart, as they all i) have the same height, and ii) use similar (pastel) colors.
"Never attribute to malice what you can blame on stupidity", but it almost feels like they are making the new cash hard to use on purpose.
But I would guess from a public relation perspective, asking a whole population to replace their coins just to make it cheaper and easier for banks is a harder sell that arguing security.