There are so many great reasons why you need to get an Aviator Harness and start taking your parrot outside!
First of all, safety! No matter how bonded your parrot is to you, no matter how well trained it is, no matter whether its wings are clipped or not, any parrot can accidentally fly away and be lost outside. Quite likely your parrot will not be able to find its way back to you and will not be able to survive on its own. For this reason, a leash is a great safety net.
Now I certainly don't recommend using a harness as a primary means of keeping your parrot from flying away. Your bond, relationship, training, etc should always be the main reason that your parrot chooses to stay with you. The harness is merely a very unlikely backup plan just in case anything unexpected goes wrong. Think of the harness as a seat belt and not as a chain. Just because you wear a seat belt, isn't a license to drive dangerously. Instead, it is only an important line of protection in the event that something unexpectedly goes wrong. Some folks make excuses not to wear a seat belt, maybe even calling it uncomfortable, but it is the best safety catch in the event of an accident. Likewise, for your parrot's safety it is a reasonable compromise.
That said, the harness should not be a point of torture. Forcing a terrified parrot into a harness just for the purpose of taking it outside is cruel and counterproductive. The bird will be so distraught by the harness on its body that it will not have a chance to notice or enjoy the surroundings. This will also harm the parrot's relationship with you. It is better to take a parrot out in a travel cage or not at all than to mistreat it by misusing a harness. But, there is a way to teach the parrot to wear the harness voluntarily.
Parrots are very intelligent and capable learners. So if we teach them the purpose and method of putting on a harness such that they agree to wear it, then there is no problem. The most important thing that I teach my students is to ask the parrot if it agrees to wear the harness and until the parrot says yes (through its behavior), you are not to make the parrot wear it. Instead, I teach parrot owners how to use positive reinforcement and a carefully developed training regime to teach the parrot to want to wear the harness.