Philadelphia Public Schools allow open enrollment just like Archdiocese schools. My guess would be it comes down to money. Philadelphia Public schools are operated by one school district so the cost is all the same. I believe the rule is if there are open seats in a school any Philadelphia resident can apply for that open seat and the decision is made from there. I think more than half of the students in Philly Public schools attend a school that is outside of their designated school.
I actually can explain this process pretty thoroughly. All 8th graders in Philadelphia are required to apply to high school. Kids are apply to a maximum of five public schools (outside of the charter system - and they don't need to apply to their zoned public school). Applications are measured by PSSA scores, 7th grade transcripts, behavior and attendance data, and essays. There are four tiers of selectivity (in descending order)-
1. Special Admission Schools (Central, Parkway, Masterman, etc.)
2. City Wide Admission Schools (SLA, Carver, FLC, etc.)
3. Any zoned public school that isn't yours
4. Your zoned public school
Every student is guaranteed a seat the public school in your zone, but you can apply to seats at another one. Those applications get reviewed for acceptance, and schools are not required to accept students even if they have open seats. Academically, George Washington and Northeast get a lot of out-of-zone applications because they are the only zoned public school that have IB Curriculums, and Frankford has a specialty career prep program (you can get your pilot's license at Frankford, for example) that gives it a greater than average out-of-zone kids.
The city wide and special admission schools don't have any geography they pull from and 100% of their students come from the application process. Special Admissions are particularly selective, require recommendations, and often have additional criteria beyond the application process (Masterman, for example, requires 2 years of a foreign language for admission). City Wide Schools are often speciality programs (Science Leadership Academy, GW Carver School of Engineering, Dobbins Tech, etc.) or offer a wider array of things like AP courses compared to local schools. So while yes, it's true that greater than 50% of the kids in the city don't go to their local school, more than 50% of the high schools (27 of 49) in the city are not local schools.
Getting on my soapbox for a second - one of the issues in the system is that the zoned local public schools are schools of last resort. Any kid in those zones who can get in anywhere else will go somewhere else, so what has happened is the local public schools have exclusively become places for students who did not get admitted elsewhere (save for the ones I mentioned above). So by design, they have the weakest students in the city, then get dubbed "failing schools".