One of the biggest requirements of the MPL scheme is that the student is carefully assessed and selected and is training towards a specific type and to company SOPs. A self sponsored MPL would not work well as it is difficult to train a student for a generic type, ATPL would be far better in that case.Plus the cost would be greater So it wouldn't make sense.
Don't get me wrong, MPL was never designed to be the replacement for the ATPL route as it doesn't cater for other disciplines like the single pilot world. It was purely designed to provide job specific training to airline pilots.