First: I am not against the use of protection filters, nobody should be, as there are many circumstances where it is wise to do so and everybody is totally capable to judge the way in which he/she wants to use his/her equipment. Some people wear away the paint on their car by polishing it every day, others never even wash it, causing it to corrode away. Both are equally wrong 😉
I already posted part of this some time ago; it has been expanded.I put it into another thread first, but moved it here.
Any lens has internal flare because of reflections. The better the coatings of the lens, the smaller the intensity of the reflections and with that the degradation of the (theoretically possible) image. One would think that the addition of two reflective surfaces to an optical system with, say, six elements is not that bad, but unfortunately the number of reflections is governed by one of the optical laws of the 17th century Dutch astronomer/physicist Snellius which is R=N(N-1)/2 where N is the number of air/glass surfaces. So a Summicron with 6 elements and 12 surfaces has 66 [ 12(12-1)/2 = 132/2 = 66 ] reflections. If you add 2 surfaces you will have 91 reflections [14(14-1)/2 = 182/2 = 91 ]!Just try stacking filters and adding four or even six surfaces in this formula. Depending on the situation this may really influence contrast. Lenses with more elements and/or less effective coatings will be even more at risk. This is about the type of flare called veil, which usually can only be seen in direct comparison, as it is an overall degradation of the image. The type of flare that produces "UFO's" or diaphragm reflections, is of course well known, but it follows the same laws. Then there is direct reflection of the filter called ghosting, which will result in highlights being reproduced once at a certain distance of the original image, often upsidedown. We had some beautiful examples of that in the RD1 forum a while ago with a Summicron 35 and Hoya filter. Not the worst combo by any means. All these types of flare will be reduced by modern coatings and will only be apparent in adverse circumstances, that is high contrast situations and photographing against the light. It is wise to take a protective filter off any lens in those conditions.
The next problem is especially with wide-angle lenses: The light travelling at right-angles to the filter will have a considerably smaller distance to go through the filter than light striking it at an acute angle, resulting in a difference in refraction and with that in loss of sharpness. It is a widespread misconception that a planparallel surface is not a lens. This is incorrect. It can easily be demonstrated by standing at the middle of the long side of a swimmingpool and looking in. If you have removed your kids from the water and there is no wind, this will form an ideally flat surface, comparable, even superior to, the filter in front of your lens. Now look at the bottom. Instead of the rectangle it is, you will see it distorted into a barrel shape. That is caused by the centric perspective of your eyes turning it into the equivalent of a concave lens. The same thing, and similar effects, happen with anything photographed at distances closer than infinity through a filter which is exactly what one is doing with wideangle lenses. It interferes with the rectilinear rendition your lens is trying to achieve, throw the corrections designed into the lens out and will introduce chromatic aberration as well, as the distortion is wavelength dependent.
Do lens manufacturers do something about this? Mostly the effects are small and hardly noticable, so only some of the very best -and expensive- lenses have been designed with this aspect in mind. A few Leica R wideangles have a built-in filter turret and no filter thread, enabling the designer to compensate fully but the most interesting examples are, of all things, Leica's top tele range. Take for instance the 280 apo 4.0. A fully diffraction corrected lens. Any interference with the path of the light would throw the correction out. So Leica made the front element the least expensive and a fixed protective one, fully correcting for it in the design and added a filter-holder at the rear of the optical system, which must hold a filter - any filter but normally a clear one, at all times to maintain the full correction of the lens.
In my opinion and experience a lens hood and lens-cap when not in use offer far more protection than any filter without having the chance of degrading the image and as a last resort there is always insurance. But, in the end, if one feels more comfortable with a "protective" filter and is happy with the results, what reason would there be to do otherwise? As long as one is aware of the theoretical considerations, that , as always, must be subject to the final result. And remove the filter and use a lens-hood in any high-contrast situation.
The reason for using a lenshood, apart from the obvious advantage of reducing the amount of light that shouldn't be entering the lens in the first place, is that it cuts off a proportion of the so-called "skew rays", that is rays that enter the lens at an oblique angle to the optical axis. Those are the most difficult ones for an optical designer to compensate for and thus the hardest for the lens to handle. Using a lens hood will improve lens quality in all cases, even when one thinks it is not needed.
Just for completeness sake, a filter for UV protection is not needed with nearly any post-1960 lens, as the lens kit in the kitted elements will provide adequate UV protection. Except the 2.8-90 Elmarit, which has no kitted element and is protected by coatings only. That one will benefit from a UV filter in the mountains and on the beach, as may some lenses from other makes that I do not know about.