I saw one recently where the cyclist shouted out something like, "ON YOUR LEFT!" and all it did was startle the crap out of a jogger who spun around into the path of the bicycle. Luckily just a close call. That cyclist's "warnings", with no time for pedestrians to react properly, were really just a game of Russian roulette. (And really rude, as you say).
You're either traveling slow enough that it's not necessary (and why yell at people if you have to?), or are too far away for someone to understand and get a bearing on who isn't already looking at you.
A bell is still rude in a shared space but used correctly, a decent one can at least be effective.
Being visually impaired, though, I'm grateful for cyclists who use their bell. It's immediately clear. For some reason, my brain takes slightly longer to process someone yelling "on your left!" or similar, than just a quick "ring ring".
I just don't think that is even a little bit true, or at least it's something that is very culturally specific and thus not generally applicable.
I have a friendly sounding bell I use from an appropriate distance (and I can modulate the volume), and I routinely have people give a light wave to show they heard. In addition, the biggest complaint about cyclists in local social media is about them passing without notice.
A gentle bell mostly doesn't do that.
On US forest trails, the general rule is bikes yield to pedestrians and everyone yields to horses.
(Obviously pedestrians walking in bicycle lanes are doing it wrong.)
> § 11-1512. Bicycles on sidewalks. (a) A person propelling a bicycle upon and along a sidewalk, or across a roadway upon and along a crosswalk, shall yield the right of way to any pedestrian and shall give audible signal before overtaking and passing such pedestrian.
https://codes.findlaw.com/il/chapter-625-vehicles/il-st-sect...
No idea if the lakefront trail is classified as a sidewalk but there are at least some cases in Illinois where either a bell or a "on your left" are legally mandatory.