Yeah, this has been a problem for a very long time. I eventually stopped adding subtitles unless I need them. Thank you, CC for bringing this up. I did not, because I did not think anyone would really look into it. Honestly, Menu creation is one of the worst functions of DVDFab Creator, and apparently they are not improving this anytime soon as menus have sucked for years. They do not burn well and do not work well when you play a disc, so the 'Streaming' menu is now the only one I use, and even that one is lacking (as you stated).
Mediafan
A workaround that works- put the file(s) into Tsmuxer and create a "dummy" .srt file that comes before the actual .srt - So when the files are finished in dvdfab w/ streaming menu, it will still default to subtitle on- but the dummy subtitle with nothing on it will be the first default sub, and will show nothing.