I've been assigned to the "time to staff" file for a half-dozen years now, examining both what makes it faster and slower in the Canadian federal system, as well as applicant and manager perceptions. I should qualify what I say by noting that we only survey federal public servants. So, we hear from people within the federal system and those who have recently entered government from outside, but have no data from those who applied from outside, waited, and decided they could not afford to wait any longer. And naturally, since the only reason they can provide us with an opinion is because they landed a job, their opinions should be viewed within that context.
One of the patterns I routinely see is that applicant satisfaction with time required for the process declines with time taken (no great mystery there), and those folks with more irons in the fire tend to be less satisfied with how long the process took. We assume this is because they view feedback about the process as urgent information they need to make a decision among multiple possibilities ("What if I accept this offer, and another better one rolls in 2 weeks later?"). As you can imagine, the folks who apply to lots of things are younger and at earlier career stages.
A second pattern observed is that often it isn't the time it took, but rather how much radio silence there was. I often see complaints from people about waiting lengthy periods (and our staffing times are little different than yours) with no feedback about where the process is at, what's coming next, or their status within it. Better communication with applicants, and updating them on the progress of the process, or reasons for it stalling, would do much to maintain their interest. It should be honest information, though, and not turn into the Seinfeld "Chinese restaurant" episode, where one gets repeatedly told "only 5 more minutes".
Allied with that is the need to do a better job explaining to external applicants what is involved in public-sector staffing. Private-sector employers, who enjoy the advantages of at-will employment, can make quick offers because, if you were a bad choice, they can dump you just as quickly. Public-sector employers generally intend on a long-term commitment and so have many more steps to the selection process so as to avoid (as much as is possible) a "30 year mistake". Given that the brunt of younger external applicants' work experience is with employers who are fairly slapdash in their selection procedures, there is an immense contrast. Yes, we can streamline things a bit, but we also need to still explain why the difference between hiring procedures in this sector vs that.
One of the things I tend to see is that the longer hiring takes, the longer it takes. If a manager can "get in and out" quickly, they will have staffed within a steady-state landscape. That is, the circumstances in place when they realized they needed to fill a position are the same circumstances in place throughout the process. If any aspect of those circumstances changes, that slows things down, which in turn increases the likelihood that something else will change and delay progress even more. That change could be organizational budgets, approval procedures, management, HR staff, etc. If there is a board required to interview candidates, one or more of the board members might become unavailable. We should also note that managers staff on top of this whole other full-time job they have of managing their unit, and their other full-time job of having a life. So work or personal commitments can insert delays. Again, the odds of any of this happening increase with the amount of time initially required. If you're a private-sector employer and can make an offer within a week or two, chances are pretty good none of those interferences are going to crop up.
Federal staffing processes can be VERY large and involve a great many applicants. The larger the number of applicants, the more time things take. The people who make an offer within a week may only have 8 files to go through, rather than screening 800.
I looked at our data, breaking it out by occupational groups, and was surprised to find that, while there were a number of factors that could be reliably associated with increased staffing times in the aggregate, different clusters of factors tended to matter for different sorts of jobs. So, for example, some kinds of jobs in the capitol region would result in an applicant pool that might already meet the security requirements for the job, and not require any additional time for conducting security checks, shaving off a few weeks on average. Other sorts of positions would be specialized enough that the hiring manager would have to readvertise in order to attract enough qualified applicants. And so on. The takehome message is that there is unlikely to be any monolithic set of steps one might take that would speed up all staffing.
Finally, apart from wanting to make the applicant experience a more pleasant one, the argument we routinely hear from managers is that, by "taking so long" (and I have read that precise phrase in survey comments thousands of time), they fear they are losing out on the best candidates. We should bear in mind that, unlike the private sector, government is not in competition with anyone for market share, such that if government doesn't land that hire, the competitor gets them. Lightning hiring speed matters in the private sector, but not as much in the public sector. We ask managers in our survey how satisfied they are with the quality of hire (if they have had enough opportunity to observe their performance), and also ask if the first candidate they made an offer to turned them down. Managers' satisfaction with hire quality is neglibly different between those who got their first pick, and those who were stood up by their first pick. So, while speed is pertinent to holding onto those external applicants who simply want a job...soon, it may have much less relavance to the quality of hire than we might think, based on private-sector experience and priorities.