Good question MiG. What I don't like about the PTM is that the seedlings are generally exposed to light. And seedlings raised in zero gravity environments are shown to respond to light, including root development.
So, @Viva_Mexico I’ll stipulate that gravitropism is the dominant factor influencing root development in soil-planted seeds. But phototropism is the dominant factor in shoot development, and can be the dominant factor in root development in the absence of light, as this NASA experiment on the Space Station showed.
These are seedlings grown in zero gravity in clear agar, exposed to light from one end. With no gravity at all, shoots grow toward the light, roots away from it. Exactly the same as in gravity environments.
The full video is here. The relevant part begins around 7:00 in.
Roots use gravity, but don’t need gravity, to grow correctly. Exposing root tips to light, such as in the NASA experiment, or with “PTM”, can initiate phototropic responses that can compete with or replace gravitropic responses. That, combined with the 2-D sprouting substrate of a paper towel against a plate, plastic container or bag, is likely why PTM seedlings develop curled root tips.
@Viva_Mexico, since you seem to have a strong preference for ex situ germination, maybe you can explain, what is the benefit to the plant of ex situ germination? Other than giving anxious seed-poppers something to look at for three days, what is the benefit?