Your example is a bit confusing because it seems to be a GPS-based route, it may be better to a look at a more 'realistic' one, where you're using only VORs for navigation. The reason to tune a second VOR is to cross-check your position, either by crossing a specific radial or perhaps by using DME (for a VOR/DME or VORTAC). If that's useful to you then you should definitely tune it.
Here's a US example. Let's say I'm flying eastbound on V241 from the SJI VORTAC following the 081 radial outbound. I've tuned the SJI VORTAC on NAV1, but I have no DME or GPS:
ATC tells me to "report LOXLY", which is 29nm from SJI but I have no DME so I can't report based on that. However, LOXLY is at the intersection of the SJI 081 radial, the BFM 052 radial (BROOKLEY VORTAC) and the NUN VOR 305 radial. That means, on NAV2 I can tune either BFM 052 or NUN 305 and when both the NAV1 and NAV2 needles (as it were) are centered, I'm at LOXLY. You might also notice that the PENSI intersection to the east is defined not only by VOR radials but also by the localizer on runway 17 at KPNS.
In this example, two VOR radials are needed to identify the fix (assuming no DME and no GPS) but you could tune a second VOR even if it isn't required for a named fix, to manually check your progress along your route (see chapter 7 of the FAA Instrument Flying Handbook). You can also time how long it takes to cross two radials on the off-airway VOR and use that information to calculate the distance to it, as a sort of 'manual DME'.
Having said all that, if you don't need or want position information from the second VOR there's no reason to tune it. But especially if GPS is your primary navigation method it wouldn't hurt to stay familiar with them as a cross-check and even as a fallback in case GPS becomes unavailable (which is not unusual).
(As Carlo Felicione mentioned, you could use just one NAV radio and switch back and forth between two VOR frequencies, but that's rather awkward and not something that most people would want to do in normal circumstances.)