Is it a trap for travel agencies to offer free tours?

most of the free tours offered by travel agencies are tourism promotion or -group shopping tours.

It is suggested that except for large travel agencies or travel websites, everyone else should be alert.

there is no free lunch.

Usually, the lucky draw for tourism promotion will require you to come back and hand in your homework or broadcast it live. (basically, the requirements for being selected are that you have a good travel history before or that you are a little famous.)

Shopping groups are the traps you mentioned.