Yes, there definitely are situations when L1C is preferable!
The problem with L2A imagery is that it attempts to fill-in cast-shadows, and doesn't do it very well when they are pronounced, causing unsightly super-saturated artefacts in, or adjacent to, those shadowed areas ( a saturated 'ghosting' or 'dodge' effect: over-brightened, saturated areas that shouldn't be there — see below ). It also flattens the land relief in its attempt to counteract / standardize natural illumination. In fact, visually, L2A often makes it very hard for a lay person to make sense of the forms they are looking at.
Below, is an example of L2A vs L1C imagery ( same date ) for a section of the island of Kauai, which has extremely sharp, jagged mountains — and canyons! ...Can you tell what is going on with the relief in L2A? I certainly can't, or not well, anyway; whereas, with L1C, it's immediately obvious ( visually comprehensible — unambiguous — at a glance ).
Obviously, despite atmospheric fogging and whatnot, L1C is more realistic, if you are interested in depicting the Earth surface the way it might actually look to a human observer from up-high — with their own eyes ( assuming you do some post-processing to increase contrast, and some color-correction ).
L2A, however, might serve better as the basis for a ready-made diffuse map, aided ( multiplied ) by a "hillshade" layer, or applied to a 3D model. But, even for that purpose, I believe producing a mosaic based on dates when the sun was close to perpendicular to the ground would yield a much more realistic, and pleasing, diffuse map.
Below: a date and time when the sun was close to directly overhead, producing a nice diffuse map, with few, if any, cast-shadows:
[ Close-up ] L2A super-saturated "ghosting artefacts" in full display ( ouch! ):
In my opinion, L2A is okay in a pinch, and for some GIS applications, but visually, I wager you can't really beat L1C — assuming you take the time to process it yourself.
Note: the adjusted versions where done manually, in Photoshop, based on my monitor's gamma and color-space, so might look either too bright / dark, or 'contrasty', on yours. Some creative license for setting contrast and color-balance, in this use-case, is expected however.