A tradition that gives a goddess the leftovers is making an argument, and the argument is about access. Ordinary temple practice is organised around purity: who may enter, what may be offered, what contact disqualifies an offering, and which people are held to pollute by their presence. The rite of Matangi suspends every one of those conditions, does so on purpose, and the texts that prescribe it say plainly that the goddess is reached in this way and not in the other.
The claim being made is that the Goddess is not the reward of purity. That is not a modern reading imposed on the material; it is what the practice does, and it belongs to a wider tantric pattern in which the substances and the people that orthodox religion excludes become the means of approach. Comparable moves are made with her neighbours in the list, Chhinnamasta and Dhumavati above all.
It is worth being careful about what this did and did not change socially. Tantric ritual inversion took place inside a society that went on enforcing caste outside the rite, and scholarship has warned repeatedly against reading the reversal as a programme of social reform. What can be said is narrower and still substantial: a tradition placed a goddess of the excluded in its central list of ten, made the ordinary rules of purity inapplicable to her worship, and wrote that down where it could be read.