You do not need to attend a well-known or top ranked school in order to be employed as an OT. You need an accredited program with good internships. Over the years I have worked with many OT’s and related service providers in schools, hospitals, etc. Many of these professionals graduated from schools that I never heard of yet went on to have successful careers.
I agree that a negative of applying to a BS-MSOT program is that you are stuck (?) if you want to switch majors. That is why I asked how competitive it is to get into grad school. Some fields are very difficult- for example speech has become very competitive. If a school receives 200 applications the program may take 20-25. Not sure if OT is similar, but If it is then the BS/MS program may be beneficial.