Costs aren't exactly lower. The study noted that the cost savings came from higher student to teacher ratios in 1st-3rd offsetting higher costs of teacher training and classroom materials over a hypothetical amortization period. This is rational but not indicative of flipping a switch to save x%.
The upfront costs of teacher training and Montessori materials were amortized
over their expected lifespan of 25 y. Total costs for Montessori and
traditional programs were divided by the average number of children in each
type of classroom at the PK3, PK4, and kindergarten years, then summed to
yield the cost difference of Montessori and traditional programming over
three years of public preschool.
higher costs of teacher training and classroom materials
the current cost of montessori teacher training and materials is a matter of scale.
the training only takes one year. the cost comes from it being done on top of the traditional teacher education that most teachers likely went through.
if montessori training would be included into traditional teacher education, the cost would be absorbed (you could skip a few other redundant classes). likewise, the material produced at scale would be cheaper.
Sure, sometimes short term spending enables long term savings. And on an even longer time scale, how do improved outcomes figure in?
The significant factor is how a change like this is implemented in context. Within a public school system there may or may not be convincible political appetite to increase short term costs for longer term gains.
It seems that the district(s) studied are making those changes and studying the outcomes in order to make prudent choices long term, which is not flipping a switch but is doing more than nothing.