Without doubt one should never begin their swordsmanship training with a fully sharpened sword. Regardless of the talent or experience in other martial arts.
First of all there is the danger of injuring yourself due to the rather complicated techniques as nukitsuke (nuki-uchi~ drawing of the sword) and noto (re-sheathing of the sword in the saya). Note that your left hand is moved very close to the razorsharp blade and even a slight touch to your skin will instantly cut through it.
Secondary there is a more practical (but also possibly dangerous) thing as the damages to the saya. The groove where the cutting edge has to pass through is approximately 2 mm wide and maybe 1 - 1.5 mm high. Because of the curvature of the sword it is extremely difficult to NOT touch the sided or top of the inner saya. Doing this repeatedly will surely slowly carve out the wood of the inner saya eventually causing it to split.
Often it splits exactly where your left hand rests on the saya. Even an unsharp geometry of a iaito is sharp enough to slowly wear out the saya.