I have never used a physical exchanger because there is no physical exchanger in my city in my country. So I have no experience in this matter. Because of this I cannot provide any effective or potential feedback here. I mostly exchange my bitcoins from online centralized exchanges and cash out bitcoins using P2P services. It is very risky but I have to use it as there is no better way to exchange or convert bitcoins in my country.
I am also using online exchanges to buy and sell my bitcoins and use their P2P service to convert bitcoin to my national currency. but I don't see any risk, as long as we're not using centralized exchanges to store assets for a long time and we're using CEX for the purposes they were made for.
I also prefer online transactions to physical transactions because I feel more secure doing transactions online. Since there is no physical appearance we know that we are far from harm unlike going to physical exchanges. It saves time and effort doing transactions online aside from being safe doing transactions at home.
For identity, the comparison between online exchange and physical exchange is not different. when you use an offline exchange, other people will also know you have bitcoins, and if it's unfortunately, a government person, you'll be in more trouble.
This depends on which country you are. If you are in a country that banned Bitcoin and yet you indulge yourself in Bitcoin transactions and the government person knows about it, then you will really get in trouble because you are doing an illegal trade. While in my country, even if you are seen by government personnel transacting in Bitcoin, that person won't bother since Bitcoin is allowed in my country.