Should we inquire directly with the bank again for the mediation offer?

No, the broker always brings in customers now and then, you only come once. Who gets more pampered??

The sales agent in the bank also has to make his cut. The loans that go out through the platforms are a different profit center.

The salesperson at the bank also has to make their cut. The loans that go out through the platforms are a different profit center.

Sure, but he will not undercut an intermediary. And as already described, multi-channel; once the request is placed, the customer is tied to the intermediary.

Honestly, I find this "stinginess is cool" mentality pretty disgusting.

I go to an intermediary because they can conveniently provide me with several offers from different providers without me having to take care of it, and then I choose the one that suits me best.
But then I want to go directly to the provider and cheat the intermediary out of their commission to save a few euros.

There you go: if you want to save that, you have to do the hard work and contact all possible (and impossible) providers directly. Otherwise, I find it quite right that you then get listed with the intermediary.

This kind of attitude just annoys me. Just like the people who get long and detailed advice in a specialist store and then order online for 2.50€ cheaper.