I really must read what I have written to make corrections before posting. It's good that you understood it.
When I said protection I mean having a filter prevents physical damage to the lens.
Less so than one might think. Filters are made of thin fragile glass. They don't provide very much physical protection before they break. There are actually situations where a bare lens would be unharmed, where the broken filter might cause damage.
Realistically, Filters typically don't make much of a difference in terms of physical protection, and they don't usually affect image quality. Your lens will probably survive unharmed without a filter, and your image will likely still look good with a filter.
What they do do, is to bring out emotions. If using a protective filter makes you
feel more comfortable, then you should use one. If a filter makes you
worry about image quality, then avoid them. Frankly, how they affect feelings is their biggest effect.
Also if something lands on the lens then if there's a filter on the lens you could remove the filter and carry on photographing.
Usually, it's faster and easier to clean the front element. If you are in a situation where you are worried about something falling on the lens, then you shouldn't be taking the filter off. You should be cleaning the filter so it can continue to provide protection.
You need to clean the filter as carefully as you would the front element. As you are shooting through the filter, the quality and condition of the that filter is as important as the quality and condition of your lens.
Of course, if you are in a situation where you are worried about dust, fluids, etc., you probably want to protect the barrel more than the lens. The front element is easy to clean. It can be a disaster if fluids or contamination get under the focus/zoom rings or into the barrel. Contamination inside the lens barrel is a major problem for a lens. Such contamination doesn't enter the lens through the solid glass front element, it usually enters through breathing holes under zoom/focus rings.
In terms of protecting the front glass, use a lens hood. This is a big help in keeping fingerprints and other contamination off the front piece of glass, whether it's your front element or a filter. The lens hood also has an advantage of reducing flare (this is more important if you are using filters on a digital camera)
With programs like Lightroom and Photoshop then maybe the days of putting a filter on the lens for a certain scene are disappearing.
There are still situations where you need the filter as you can't easily replicate the effect in post processing. Polarizing filters and neutral density filters are two examples that come to mind.