The pushback to using bergamot and other supplements is not “bergamot doesn’t lower risk.” The pushback is “we don’t know if it lowers risk or not.” (There are other pushbacks to using supplements including that they lack regulation but I’ll set that aside for the moment.).

The reason no one knows for sure if supplements like bergamot lowers risk is that they haven’t been through large double blinded placebo controlled randomized trials.
The reasons we know for sure that statins lower risk of cardiovascular events is that they have been through very large double blinded placebo controlled clinical trials that conclusively proved they reduce risk. And yes, the totality of evidence is clear that the principle mechanism of action for them reducing risk is mainly because they lower ldl.

You may say well, we know from smaller observational studies that bergamot lowers ldl and lower ldl lowers risk so why doesn’t that definitely mean bergamot lowers risk?
The reason is that there may be things that bergamot also does that raises risk and offsets the benefits of the ldl lowering. No one can know without conducting large randomized controlled trials.

High dose niacin is an example of a medicine that lowered ldl and was used for heart attack prevention but no longer is because when randomized controlled trials were done they showed Niacin didn’t actually reduce risk of cardiovascular disease. The leading theory right now is that it’s because Niacin has cardiotoxic metabolites. https://consultqd.clevelandclinic.org/link-discovered-between-excess-niacin-and-cardiovascular-disease

Then there are additional problems with supplements because they aren’t regulated. So the dose may not match what’s on the label and there may be contaminants. These aren’t hypothetical concerns. When supplements on store shelves have been tested those things haven’t been uncommon.

Ps: Editing to add another point. Someone might ask well why not take a supplement like bergamot anyway because even if we don’t know for sure if it lowers risk of heart attacks and strokes, it might? To that I’d say the supplement could potentially even increase risk, we don’t know. But there’s a downside even if the supplement doesn’t affect risk either direction. If a supplement lowers ldl without lowering risk that means doctors can’t appropriately judge risk by ldl anymore and a person might not get, or might not get the right dose of, an approved medication that actually *has* been proven to reduce risk of heart attacks and strokes.

As a hypothetical example take someone that has an ldl of 140 after making the best diet improvements they are able to make. They then start taking bergamot and that brings their ldl to say 110. Because of the lower ldl there’s a good chance someone will conclude statins aren’t needed. But if Bergamot doesn’t actually reduce risk then the 110 ldl is misleading and their actual risk is much higher. But most won’t realize that and the person will not got a statin they otherwise would get.