Yes. It is allowable to turn off an auto pilot and fly an aircraft manually. However…. There are some restrictions. If you are flying in RVSM air space, you must keep your auto pilot on. Reduced Vertical Separation Minimums. This is air space above 29,000 feet where planes are typically flying on well defined routes. Such as across the North Atlantic. They allow planes to fly closer together than would normally be allowed, because the auto pilot guarantees they remain on track.
Airlines encourage their pilots to fly without autopilot to maintain proficiency. It is something airline pilots do some of the time if conditions are favorable.
When you fly with auto pilot and auto throttles, the plane is doing a lot for you. This frees up your brain for doing smarter things, such as being aware of other traffic, monitoring fuel consumption, getting set up for an approach, and generally resting your brain. Getting a pause before the heavy work load of approach and landing.
The auto pilot/auto throttle combination flies extremely well. It stays on course, it maintains the right speed, it does exactly what it is programmed to do. Setting up the route and expected navigation is a main task for pilots, and it happens before you leave the ground. The auto pilot will fly safely, precisely, accurately, and correctly if it is set up right. You get better fuel economy with AP because it continuously makes very small corrections, smoothly.
So, you want to fly by hand? Ok, go ahead. You do something wrong, it is all on you. An airliner is not all that hard to fly, it is very stable compared to smaller planes. Flying it by hand does not make much sense. You are not really connected directly in a lot of planes anyway.
I am no longer part of airline industry. I own and fly a small plane regularly. It has an auto pilot, but I rarely use it. Once I get the plane trimmed up, it flies more steady without the auto pilot. If I had more money, I would get better automation. But for now, I would rather spend the money on fuel, see another view of the ocean, fly out for another $100 burger.