This rant is based mostly on the problems that I have faced in my brief research career so far. Nonetheless, it also is indicative of the general problems that people like us, who work in small groups in places like India (by choice, of course).
Now, in research, the most tangible measures of success are all associated with publications (no., quality, citations etc.). As the maxim goes, "If your research does not generate papers, it might just as well not been done. Interesting and unpublished is equivalent to non-existent." It's like the tree falls in forest kind of philosophy. Or as the advice goes, "Do not be afraid to publish." Publications are paramount especially at the beginning of one's career -- to get a job, then to get a promotion. This is all well, except that it is also hardest to publish at the beginning of one's career, especially for people like us.
In a typical research lab in the US, at any time there are 2 or 3 ongoing research projects of reasonably broad scope. So, in a sense, when you come in, there is a reasonably well motivated problem waiting for you. Well, not exactly. During the first two years you also work on different projects in the labs before you start focussing on your thesis work. But the PhD problem you chose to work on fits into (or extends) a research project. At the least, the insecurity that 'what I have been working on may not be relevant at all,' is not there. Because, otherwise NSF wouldn't have funded it

. So, by the time you focus on your thesis, there is enough clarity to start being productive. Also, there are 3 or 4 other students working on your project. That is only going to improve your publications.
Compare this to how we start. We don't start on a research project that has already been funded; we usually start by defining our own individual research problems. Chances of working with senior PhD students are also low. So, no 'pre-existing co-authorship opportunities

Moving on, the masters students who are working on a sub-problem of your research (or on a closely related problem) may not stay long enough in the lab to bring it to a logical conclusion. Every time that happens, you again lose a co-authorship

(Not faulting master students; just stating a fact.) You are on your own more or less. Now, at what frequency can you get high quality ideas? May be one (or two) in a year. And then it takes a couple of years for you working alone, to develop them well enough to be able to publish. Then the question of what about funds to travel if the paper gets accepted arises. That itself will be a huge topic of discussion, so let's not get into that.
Instead, let me talk a bit about the problem of 'where to publish?' Obviously, in a high quality conference or journal. But as I said, it takes a lot of time to produce a work that is of matching quality. Chance are there that the paper might miss out on getting accepted (only just in many cases). A rejected paper is a big problem. Obviously, if you don't publish your work, it's as well as not done. If you are an affluent lab, you may quickly rehash the paper and send it off to a relevant workshop of reasonably good reputation; then spend time on the paper, enhance, and send it to a journal. We cannot afford to send a lone entry into a second rung workshop in a distant country.
In fact, it is these works that are 'not good enough to publish (in a good place); not bad enough to rubbish' pose a big challenge. What do we do with them? Even in my brief career, I've faced this a few times already. A couple of times, graceful (or not) burials have been given. But I can't go on doing that. After all, I have a PhD to complete, a job to get, a life to live and so on.

Even now I have at least two important research problems/directions in which there are interesting preliminary results, but they are not good enough to deserve grand publications. (Let me make say it again -- the problems are important; but there is only some preliminary work done so far.) Obviously, I should continue to work on them till there is significant contribution. Well, that might mean extending my PhD by a few years.

I am definitely not suggesting that people automatically become successful by joining an established lab. There are also people who change the course of a field during their PhDs whether they are working out of an established lab or not. I am only talking about some comparative advantages/disadvantages for an average PhD student. Of course, what matters ultimately is what you contributed, and not why you possibly could not contribute as much as you wanted.