You didn't mention much else about your father's condition: age, other health problems (how is his heart? does he have diabetes?).

Basically, if the doctors see fit, the rehabilitation has the more rate of success the earlier is started. This is especially true since, the more restrictive bed rest your father has, the more risk of incurring conditions (muscle atrophy and weakness, contractures, spasticity, urinary infections, pressure ulcers – bedsores) he is exposed to, which can make the later recovery much more complicated and problematic.

It is of paramount importance that the rehabilitation procedures be started as soon as possible (especially because developing of muscle contractures makes later mobilization extremely difficult and sometimes impossible, and because the more time the limbs remain motionless, the more time it will take to the motor cortex to be able to coordinate them again), so, particularly since your father's doctors consider him to be well enough to start, then, by all means, he should slowly begin his way to his recovery.

His exhaustion feeling may be a result of depression and hopelessness, rather than a result of the disease itself. Along with speech therapy (although you mentioned that is aphasia is mild, so it may even revert spontaneously), he should also seek some psychological counsel and guidance through the recovery process.

I hope your dad's recovery will be fast and complete and don't forget, as much as this illness is destructive and devastating, many patients enjoy a full, complete recovery.