I'll start my post be saying that my opinion on the London Mulligan is not firm. It's a complex topic and relevant data are limited. Three weeks really isn't enough to gather sufficient data to make statistical comparisons (at least with the limited data that our benevolent overlords permit us to see). So we're left with weaker forms of evidence (trends, intuition, etc.)
In any case, my initial reaction to the new rule is net negative.
There are certainly positive aspects of the new rule. As others have articulated here, the new rule may increase the breadth and complexity of decisions in the early game and in deck building. In theory, this should reward skill/experience and make the decision process itself more mentally stimulating and enjoyable.
However, several factors make me especially concerned about adopting the new rule.
First, I don't think we have (or will have) the data necessary to have an idea of how the new rule will affect the metagame and play experience. I recognize that taking risks can be an important part of improving the format/game, but I feel like the magnitude of this proposed change needs a commensurate amount of data to inform it, which I don't think we'll get.
Second, I worry that the new rule incentives strategies that are broken, fast, proactive, and all-in. This could make Vintage more like its caricature, the "turn-1 format." It may also make the luck of the die roll more important.
Again, hard to know for sure. The format doesn't appear to have undergone a cataclysmic shift in this direction. But I really wouldn't expect it to happen that fast, either. There's bound to be inertia in the decisions people make--people like what they play, have emotional attachments to certain cards/decks, and don't necessarily have the time/motivation to find out how to capitalize on the new changes.
Of course, such an issue could be mitigated through restrictions. But we all know how long addressing format issues through restrictions can take. I'm worried about Vintage undergoing such a large upheaval and how long it will take things to settle.
Finally, I worry that the new rule could complicate our long history of knowledge and theories regarding deck building and in-play decisions. Honestly, I have not thought this one through as deeply, but I don't think I've seen that discussed elsewhere (but I haven't read much on the new rule, either, so I could absolutely be wrong here).
Again, my post is intentionally full of "coulds," "mays," and "appears." I really feel like I don't have a firm grasp on this. Looking forward to reading more discourse on the subject.