Your hands shouldn’t be holding the head up. Regardless of needing more core strength or not, someone with shorter arms relative to the horses neck length will need to adjust the reins in and out more, tather than just moving the elbows forware and back to adjust the frame.
If the mismatch is so great that an appropriate following hand in walk and canter can’t be achieved while maintaining a connection, no amount of core strength will compensate, it’s just geometric reality, and the rider will either not be able to provide enough give or will end up with a longer rein that comes into a backward hand situation until the horse is more is self carriage.
Longer reins doesn’t equate backward hand situation.
It has nothing to do with a rein lenght in particular.
The reins just need to be the right lenght for the work that is being done.
It is all about posture and effectiveness.
I might have reins at 80cm and my friend at 70cm from the bit on the same horse, both lenght would be ideal for each of us to be working the horse the same way.
What riders need to do is shorten their reins enough to be working in front of them with the elbows at their side.
That’s what takes core strength.
Not holding the horse’s head, but holding your own hands and be able to control your aids.
It’s the self carriage of the rider.
Agreed: no one should be holding the horse’s head up. But hold your hands out in front of your with nothing in them such that (because you have short arms) you upper arms need to be in front of your body. I submit that in that position, you’ll still get tired faster than the person with long arms whose upper arms fall closer to the vertical when the hands are in the right spot ahead of the saddle.