The issue of cash flow also needs to be considered.
Some folks, especially when they first start their getting their financial ducks in a row, have expenses that are too high for their income. They have very little wiggle room in their monthly budgets. Anything that goes wrong is a real problem.
In that situation, longer term savings are less important than short term relief from budget stress.
Once the budget has a comfortable surplus by paying off some quick wins and freeing up cash flow, it can make more sense to switch away from the smallest debt first approach.
The other issue to consider in these circumstances is whether the debt is secured or not; and whether the debt is easily dischargeable in bankruptcy, should that unhappy event be necessary.