Re: hit&run
The style of the turban depends on the region in Punjab you're from. Your first pic shows a Patiala styled turban, also known as the Shahi Dastar. Your second pic and video shows the turban style worn in Amritsar and the Majha region. So called "Bhapa" style is simply the turban style worn by Sikh migrants from regions now part of Pakistan. Next generation of Sikhs in England have made their own style, often called the "Englandi turban", and same with the Americas.
There isn't really any "bad style" or "good style" of wearing turbans in general terms.
The second video I posted actually shows the guy wearing a Dumalla, the Nihang turban, and the height is actually quite normal, if not small, if you compare with normal Dumallas, especially the ones worn in Punjab. I'm sure if he found the height too much for day to day work and ease, he would change it. There's no restrictions.
I don't know what has made you touchy.
Its a good thread, people are free to add their experiences, post more pictures and videos and their likes, diversify the thread ultimately giving more inputs about Sikh Turban for larger readers.
In general terms ?
Then generally the purpose is to cover the head and people in subcontinent have been doing the same with different styles of turbans in different parts of India. The Khalsa Turban is more popular and has given it a very distinct recognition as Sikh Turban amongst all the other turbans. There are two types one is formal and other is casual. Dumalla and Parna is casual style and Shahi turban and Khalsa turban is formal. Dumalla is accepted as formal for baptised Sikh women.
There are good or bad style popular in Sikh youth boys in Punjab and Girls too. I know it because I am from Punjab, have Sikh friends and know a lot what Girls studying with us liked more.
The popular turban in Punjab is in the second Picture, Khalsa Turban, its popular in Majha, Malwa and Doaba every where. The Shahi Turban is not that popular even in Patiala now a days. The one shown in First video may be popular in Canada but I have seen Sikhs in Punjab disliking other styles especially of foreign returns. The so called (as you said) Bhapa style is printed Turbans either with Shahi style but nowadays the one in your first video.
Navjot Sidhu is from Patiala but he doesn't wear Shahi Turban rather Khalsa style but bit short of cloth lenght and little flat at the apex. There was a row few years back when he openly disliked those style.
Yes I know there is no restriction but I don't like those styles, may be I have grown up with seeing better styles, I myself know how to wear a Khalsa Turban but not that proficient and fast like my friends. My college conducts Turban wearing contest every year so I know quite other styles too including Turla Turban for Bhangra which I have wore myself and its tighter than any other Turbans.
I have seen few youth in Sydney wearing ready made Turbans like Akshey Kumar did in Singh is King and they look odd.
Dumalla is also called Nihang Singh wala Dumalla or gole (round) turban so I wrote it Nihang Turban in English. 'Parna' turban, is quickest style with shortest cloth.