And, yes, that's true as far as it goes.
But the focus on whether Hagel will be confirmed (and he'll still need some Republican votes, or else a GOP willingness to allow confirmation by simple majority) misses that what Schumer was up to was a perfectly legitimate and meaningful part of the nomination/confirmation process; in fact, it's exactly how the process is supposed to work.
That is, Schumer had some concerns about Hagel and perhaps about administration policy more generally, and he used the confirmation process to press Hagel for commitments about the things Schumer was most concerned about. In this case, it was mostly making sure Hagel was on board with stated administration policy (and, perhaps, that stated administration policy matches actual administration policy). At any rate, technically Schumer could derail the nomination or at least severely delay it by deploying all the tools Senate rules give him; in reality, however, what those tools do is give individual Senators leverage to press nominees on specific issues of interest.
That's how it should be; executive branch agencies and departments are supposed to be responsive to both Congress and the White House. And the whole idea of single-member (or I suppose dual-member in the Senate) districts is that various different discreet interests will be represented in the way that they really might not be by the president. Granted, I'm not sure how much actual policy commitment is going on in this case and how much playing to the cameras, but that's okay, too.
When it comes to Senate reform, that's why I have no problem at all with holds on nominations. Of course, holds are backed up by the ability of individual Senators to object, and the Majority Leader could move ahead using the cloture process. But as long as Senators who place holds are seeking to actively represent some particular interest (and not just a partisan opposition), then I see no problem with it.
On the other hand, there's really no reason that a minority should be able to permanently defeat an executive branch nominee -- so cloture should, in my view, only require a simple majority in these cases.
And again: the interest of the minority party is mostly just position-taking, which is perfectly served by opposing the nominee and then losing a vote.
All of which is just to say that this is the easiest part of Senate reform: for executive branch nominations, all that's really needed is to reduce the cloture requirement to a simple majority. Toss in reduced (or use-it-or-lose-it) post-cloture time, and you've solved almost all of the problem.