Well, direct democracy obviously won't necessarily give you progressive results, when people are really conservative in their thinking and goals. It will give you more conservative outcomes then.

And of course from a universal rights standpoint that regards some things as non-negotiable it is always dodgy to leave or put up rights, especially minority or marginalized peoples' rights, to a vote, no matter the voting method. So I'm not sure the direct democracy can be blamed for the long lack of universal suffrage in Switzerland. That kind of problem you can run with most systems.

But Brexit wasn't that kind of question, like asking about capital punishment in a referendum. The objection you see to settling a question like Brexit in a referendum is that complicated national policy questions are somehow fundamentally unsuited to referendums because voters aren't informed enough to understand and communicate what they want in such a micromanaging way and that it should only be done via delegation through intermediate professionals aka politicians. And I think that actually is not true, and that Switzerland shows that you can have a stable and functioning democracy with a lot of direct referendums including complicated stuff, but the system needs to be designed for it, so that the questions put to voters are sensible and the voters are involved that way consistently.

But this referendum as gimmick stuff in a system that is designed to work via delegation is like getting the worst of both systems. Especially if you throw in just one referendum and at a point when many people are discontent with the representation. Then you get this kind of angry muddle and neither the question nor the representation issues get solved, because both get so mixed up.