Another advantage might be the curriculum that a larger school might be able to offer. In a smaller school, there might be enough students interested in particular subject--say, creative writing, or space science, or art history--to warrant offering it as a class. In a larger school with a larger enrollment, more students might be interested in such a specialized class and it might be easier to offer. Generally speaking, larger schools tend to have more diverse course offerings.
Large, regionalized high schools are like small cities, and they draw prospective families into the district as much as anything. In this way, they are real estate investments by the community to maintain property value. "If you built it, they will come" is the driving strategy here. The biggest, newest, shiniest high school will attract the more desirable new families.
Also, large high schools take up less land and incur fewer costs than many de-centralized schools. It's all about overhead: limiting maintenance costs and squeezing every dollar out of every square foot of space.
I assume by regionalized you mean a school that involves several communities as opposed to each community having their own high school. One example would be a financial one, the district would have a larger tax base and most likely a higher assessed valuation than just one community. Another reason is that you could share the resources of specialized employees such as Speech and Language Pathologists, Social Workers, etc. A third reason would be that because of the increased finances the regional district should be able to offer a wider variety of courses to appeal to all students. While we are talking about advantages here be aware there are also plenty of disadvantages also.
Perhaps you need to be more specific with what you mean by regionalized high schoolsDo you mean the curriculum taught is particular to the region where the school is located? 1)Subjects taught would be more relevant to the children living in the community and attending the school—however, it might limit the knoweldge and meaning the need for life lived outside the community if they choose to leave the community in the future.