Use of railway=crossing/railway=level_crossing on trams seems to be common practice world wide. So there is definitely no consensus not to do so.

I'm not sure this is implementable with the software infrastructure for carto

It would be - we do that for turning circles at the moment (rendering them in a design adjusted to the intersecting road).

Considering how widely these are mapped and how significant they are often for navigation i would be skeptical about removing rendering. But adjusting the starting zoom level or the symbol specifically for tram crossings might be a good idea.

Beware, that this tagging very likely is not something, that individuals knowingly applied. For some time, the validator of the iD editor did add the tag to intersections tram/highway, when people answered "Yes" to the question "Do you want to connect the ways?"

Meanwhile, the validator uses https://wiki.openstreetmap.org/wiki/Tag:railway%3Dtram_level_crossing instead. in the history graph you can easily spot, when the change happened. That makes me wonder, how /organic/ the other numbers are. http://taghistory.raifer.tech/#***/railway/tram_level_crossing&***/railway/level_crossing shows some coincidence: As tram rises, the uptake of railway slows down. I'd say, this can be fixed in tagging.

1. Reasoning why I would prefer tram level crossing not to be rendered

Let's have a broader view on the topic.

It's the very nature of a map to show ways of any kind. When ways cross, the crossings are depicted by - surprise - ways that cross each other. Streets cross streets, bicycle lanes cross footpaths, bike paths cross streets, etc. In none of these cases, we show a special marker for the crossing, (not even for marked crosswalks so far). In my opinion, a street crossing a tramway track is no different (at least in the usual case, where there are no special signs, barriers, or traffic lights).

Of course, a level crossing of an actual railway with a road is a different story. It usually has physical features associated with it, such as barriers and/or traffic lights. For navigation, it is very important as it may increase travel time significantly. So the tagging and the rendering is absolutely valid for actual railway. The same holds for tram level crossing when an additional tag like crossing:barrier/bell/light/saltire is set.

2. How to achieve 1. in the best way

I also think that most of the respective tagging occurred due to respective suggestions / warnings by the editors, which used to be too unspecific. In the meantime, the editors seem to have switched to tram_level_crossing, which we do not render. So one solution would be to replace level_crossing by tram_level_crossing everywhere. But it does not feel okay. tram_level_crossing is a disputed tag, and whether the level crossing is for trams can be determined automatically. So I would love to solve the problem by having the renderer making that decision automatically.

I have opened a PR that would improve the rendering as suggested. Rendering tram crossings in case there are traffic lights mapped, would require an extra DB column, though, AFAICT.