The directors around me who start on the August 1st timeline have said that it's a con for the length of rehearsals there, but they've had some advantages in having all of their kids back. Especially if you're in a situation with poor summer attendance you may actually benefit there.
The bigger impacts are the ones that I think get overlooked - certification. Districts can determine their own level of believing someone is 'highly qualified.' This hasn't backfired in my district too much yet, but I would suggest that is one of the biggest DOI potential problems. Being forced to teach classes you aren't really qualified to teach, and there being no consequences for the district.
If your district is looking at going to DOI status it wouldn't be alone, from what I recall the majority of districts in Texas have now gone that way. See if you can get ahold of the districts plan to determine which of the options they took/are looking at. If you haven't already read the FAQ from TEA this could be helpful: https://www.tasb.org/services/legal-services/tasb-school-law-esource/governance/districts-of-innovation/documents/districts_of_innovation.pdf