Even in districts with robust charter sectors in states without voucher programs, when dollars follow bodies, inefficiencies result. Running multiple parallel systems (district and charter, not to mention multiple charter programs) results in higher administrative overhead and less money left over for student instruction.
Driving School Choice
Claire Fontaine

Clearly, you didn’t read the study you link to support your claim.

In an interview with Avi Wolfman-Arent of WHYY/Newsworks, Bruce Baker admitted that his study (the one you’re citing) did not find any evidence to support the contention that the outflow of students to charters resulted in inefficiencies and higher administrative costs for districts. On the contrary, he found that districts were largely able to consolidate administrative and overhead costs in response to the loss of students to charters.

To quote Baker: “I found for the most part that the districts I was looking at on those particular issues adjusted reasonably.”