Apple is practically the most antithetical to "free software" company around, yet Apple maintains perhaps the largest fleet of local-first apps in existence, e.g., off the top of my head: Calendar, Contacts, Keynote, Mail, Notes, Numbers, Photos, and Pages (these are all examples of apps that support multi-device sync and/or real-time collaboration).
I think the truth of your statement is more that free software tends towards what you might call "offline" software (e.g., software that doesn't sync or offer real-time collaboration), because there's more friction for having a syncing backend with free software.