Nothing prevents anyone from trying. There are many similar video platforms like Youtube. Vimeo, dailymotion, just to name two.

The legal aspect is probably the most difficult to handle for an independent competitor.

While Youtube (Google) just doesn't care or pays fees and fines, smaller competitors would have to make sure this doesn't happen. They don't have the financial basis to pay for it.

The potential competitor needs a sustainable business model. For almost all Google apps it's online advertisement. It's difficult if you have to rely on outsourced networks, that take their share.

A subscription model won't work for 'amateur' videos. To be honest most videos on Youtube aren't worth watching. The most famous ones are pushed by big companies, even if they look Amateurish and/or 'Authentic', there is a huge industry behind it.

Brand recognition is probably the least important criteria not to build a competitor, in my opinion. In the digital world the masses move from one attraction to another. I bet Facebook, Youtube, Twitter and all those well known companies won't exist in this form in 10 - 15 years. The product-life cycle of the digital world is very short. Like reddit is popular now, there were hundreds of forums like this before reddit and there will be many after reddit.

In business science it is said, that the bigger the company the less agile it can react to new trends, while competitors can grow under the radar of the big competitors until they reach a momentum. Before Google Search there was Yahoo and Altavista and many others. Before Chrome there was Netscape and Internet Explorer. Before the iPhone there was Nokia and Ericsson.

If you have the skills find a feature and code a new video platform. :)