These are two different things, and I think it's important to distinguish between them. Rapid-static isn't real-time, so I don't think it belongs in this discussion, DPOS or otherwise. My comment about getting laughed out of the room pertains to implying that a good RS solution is something only the Triumph-LS can deliver.
I agree that *if* you can get a verified RTK solution you'll save time over having to set rapid-static points and returning to the site, if that meets your comfort level. (I don't trust a single RTK shot for control work, so I generally get two or more, preferably on different days and at different times of day.) The times I've tried for 10 minutes or more without getting a verified shot, I've chosen to cut my losses and get the shot by other means. But I can usually drive to my control points; if I had to pack very far, I'd likely change my approach.
Jim raises a good point here. We all typically find a niche within which to work. I currently do not have a robot because my current work would not justify owning one. I have had a robot in the past and it is extremely efficient in many environments and under varying project requirements (i.e. incredible vertical accuracy). If I were surveying numerous small sites with a lot of sky obstructions, RTK would not be the most efficient tool to use. I've used my total station entirely on four or five jobs in the past year because RTK simply wasn't the best tool. All were fairly small in size. Two required vertical accuracy under canopy that I didn't believe RTK could do as quickly and reliably as the total station. I've also surveyed several large acreages (100+ acres) in the past year (by myself) that I simply could not have done without RTK (specifically the Triumph-LS). And there have been several jobs that were a compromise. RTK made the most sense for most of the job and the total station would have made more sense for part of the job, but I did it all with RTK because I didn't want to switch gears in my workflow for a small number of points. And there have been times that I've used a mix of RTK and the total station with great success.
My point is that surveying is so diverse that there isn't yet a single tool that does it all. This makes surveying fun though, in my opinion. Every day you size up your job and determine the procedure you'll take based on the project needs and the tools at your disposal. A ten, or even thirty, minute observation on every point may seem ludicrous or may seem like cheating depending on what's between here and there. This week, I've been working on a topo of a future industrial site (approximately 20 acres), a survey of a heavily wooded 200+ acre tract, and a cut-out of 5 acres around a driveway, house and barn from 29 acres of mostly pasture. I've used the LS exclusively on each one. While there isn't a complete do-it-all tool yet for surveyors, the LS comes really, really close for my niche.