There is nothing wrong with keeping emergency fund and back fund together. But if you keep them together then you may face some problems like if you keep your emergency fund and back fund in the same account then if your account gets locked then in this situation if you face any emergency then you may face some problems.
You really have a good point here and again another reason why I think or feel is not good to keep your back up and emergency funds together is because you can easily misplaced it by either using back up funds for emergency funds or using emergency funds for back up funds and it will be very wrong to do that because your investment is at stake.
I think emergency fund and back fund should be kept separately. If you keep them together then if you do not have proper financial management skills then you may confuse the two things. Emergency fund is money kept for personal or family needs and back fund is money kept for future in any personal or business sector. If you do not have proper financial management skills then you may spend all your money in emergency fund or back fund. So it is better to keep emergency fund and back fund separately.
No matter the level of financial management skill I don't think is good to keep both finds together and I think you are mistaking the funds. First emergency funds is not necessarily money or funds kept for personal or family needs rather it is a funds kept for those unforseen circumstances that may likely come up during one's period of investment while back up funds which I think can still be seen as a reserve funds are funds kept to handle or take care of issues aside emergency.