The hitch needs to be securely attached to the vehicle. Some heavier trucks have bumpers that are strong enough to support a light trailer hitch, but most cars and lighter vehicles need a mount that bolts to some substantial part of the body.
Duct tape and velcro aren't going to cut it.
There are also systems where the mounts are hidden from view, and you can remove the actual tow bar from a receiver under the vehicle by pulling a pin out. But the mount remains fixed under the vehicle.
Yes. There are "clamp on trailer hitch assemblies that fit SOME vehicles. Look under the rear of your car and see if there are actual frame rails under the body near the tail end. (NOT the bumper, or bumper mounts as they are designed to come apart in a wreck and clamping a hitch to them will tear them off.)
If you have frame rails, there are hitch assemblies that have clamps that lock onto the rails. Be advised though that you must periodically check the tightness of the clamps during the use of the hitch assembly and they are not as strong as a permanent type.
Let me rephrase that, is there a way to connect a trailer to a vehicle without having a permanent hitch attached to your vehicle?
Older cars could accept a bumper hitch that could be temporarily clamped to the bumper. Today's cars don't have that style of bumper anymore.
Not legally. Like rope the trailer to your back bumper?
All commercial trailer hitches are bolted on, hence can be removed.
Yes, but not safely. When bumpers were actually metal you could get one that bolted on, but they tended to loosen up on you. Today with plastic ones…well…
A thought shared.