Pretty much at every stage of my career there have been team grants of some kind, offered by institutions, states, federal agencies, industrial funders, what have you. The idea behind these sounds good: "Collaborations encourage creativity and interdisciplinary science, which is good. If we mandate that people must be co-PIs to get money, we can encourage collaborations." In practice, many team grants turn out to be ways that two or more PIs can fund their individual research on a theme that vaguely connects the two or more groups which really a collaboration. Being honest, I've done this too. Money is money, and sometimes even if we plan to work together if the funding comes through, there is already momentum on the solo projects, while the joint project has to start from scratch.
In my experience, successful collaborations rarely start out through formal mechanisms. Usually, I am talking to someone informally about my work (or theirs), and while chatting, we have an idea for an experiment/calculation/analysis that one of us can do on the other person's problem. Sometimes, my collaborations have started when my students have done something similar. In any case, all of my successful collaborations have started from one experiment and grown from there. In the best cases, the single experiment grows into a new approach on a problem that neither of us can tackle alone (even better if we can then get joint money for it!). Always, though, the working together starts BEFORE the joint proposal, not as a happy outcome of writing a joint proposal.
I won't say that team grants are a terrible idea, since once a collaboration begins, they are an excellent way to fund research that might be hard to get funded in other ways. Nor do I think that multi-PI grants that end up as separate projects along a theme are necessarily bad. I just don't think that anyone is really served by pretending that team grants produce collaborative science, rather than being an opportunity to support something that is already there.