As far as I know, anyone can open their account on Facebook, Instagram or any other social media. These days we see many videos on WhatsApp also. So why the author has the feeling that some videos are not allowed on Instagram. Probably the app is not known to many people. It is not that somebody is stopping them to post their videos. My brother's son who is an 11th class student is having his own Instagram account and posts many videos there and sometimes he goes on live there. Many people in rural areas are also using this site for their requirements.
Anyhow, for the information of the author, there are many apps similar to Tiktok. But they are not so popular and may take some more time to become popular among the people. The following are some such apps. Clash. Triller.
Dubsmash. Byte.Funimate.Lomotif.Cheez.Vigo Video etc.