I had a look at that link, and it doesn't by any means constitute proof that children should be encouraged to walk on tiptoes, though I agree that barefoot is best wherever possible.
I work in the NHS, and see many children for whom tiptoe walking is a big problem. In some, there is nothing that could have been done to prevent it, but in others, the use of baby walkers has definitely been a factor in the development of a tight Achilles tendon, and in some children there is no obvious precipitating factor. If the tight Achilles tendon cannot be stretched by physio, then casting or surgery is necessary. If tiptoe walking persists into adult life it can cause early arthritis of the knee, as weight is thrown forwards onto a part of the knee joint not designed to bear it. The same thing happens if high heels are worn constantly.
Walking is a skill that is programmed into the brain. It will occur when the child is ready, i.e. he or she has the ability to stand unaided, and the balance to then move each leg independently without falling over. This cannot be accelerated, and would certainly be hindered by misguided parents encouraging the children to walk on tiptoes. (Baby walkers do not teach a baby to walk, they teach it to propel itself with its toes).
Once the child can walk normally, there is no harm in occasional tiptoe walking, but if this is prolonged, contracture of the heel cord will result, and the child will not then be able to put his/ her feet flat on the floor.
Children's shoes should be flexible to allow all the muscles, ligaments and joints to be as feely mobile as possible. Start-Rite used to be terrible with their stiff "supportive" shoes, but I have recently bought a pair for my dd, as they were flexible enough. Except in unusual cases feet do not need support.
Here endeth the lesson