They still took hammers to machines and not the wealthy. The modern variant of Luddites are talking about banning technologies outright instead of uses of said tech. Also, the discussion I've seen online is almost always strictly black and white and often ignores the people, instead focusing on the tech.

The actions and words of the Luddites don't seem reflect what you're saying from my PoV.

I don't think that's true, at least not generally. To my knowledge, they saw themselves as enforcing the law. Indeed, old laws banned certain types of machines, limited who could possess them, and how many. These corporations had been influential in previous centuries, and so laws protected their interests, but also balanced the interests of individual members. (Today we would probably call it a cartel or trust, rather than a corporation.)

At the time of the Luddites, these laws were no longer enforced. They had tried before the courts and by writing government, but their lobbying was unsuccessful. So they took it upon themselves to break the "illegal" machines and again limit competition and productivity.