I think there is a sweet spot.

Too "modern" and I assume a site is using excessive amounts of tracking and playing other tricks with A/B testing different marketing tactics for services to try to milk their customers for all their worth.

Too crappy and I start to question if the site is actually secure and if they are putting enough money into IT... or if it's even the real site vs some kind of scam.

Both can be problems that erode trust, but they are different problems.

It is possible to have both great content and great design, but it's rare. Think of the Met museum website vs a tech startup. Both will have modern, fancy UIs, but the museum also has real information where the marketing site will only have design elements and simple hype statements.

That said, you probably want to judge your bank's trustworthiness by it's rating with the Federal government, which is public info. Most banks (all but the biggest) have to outsource their online banking software and it's never as slick as the big guys'.

I know that in general, the flashier a thing is -- that is, the more obvious effort that has been put into a thing's aesthetics -- the less likely that thing is to be great.

My hypothesis is it's because time and money investment was put into aesthetics at the expense of making the product or service better.

We're trained to assume that the prettier things are implemented by entities that care more for the pretty than the function the thing was supposed to preform.

Uglier, less decorated things are expected to function better, with less effort "wasted" on goals unrelated to the problem being solved.