I'm in a similar position as well. There are a few reasons why I want the award. The first is definitely the prestige. It's nice to have that kind of validation, especially during a part of the Ph.D. program when courses are over and I'm just working on the proposal, mostly on my own. It would be nice and significant bit of feedback that I'm going in the right direction. During the SSHRC grant-writing courses at my school, the instructor also drilled into us how much getting a SSHRC or CGS will shape our future opportunities. Speaking from his own experience, as someone who only got an OGS and didn't really try for the SSHRC (in an era when the OGS was worth a lot more), he seemed to really regret not having tried harder for a SSHRC. I've browsed a lot of CVs on the web, and I definitely get the sense that receiving something like the SSHRC is the norm for people who end up in tenure-track jobs. Not only that, I think getting a SSHRC will help me look like a better candidate for other awards in the future. It's all about the Matthew Effect.
The second is the financial freedom. At my university, we're guaranteed a decent level of minimum funding, and getting the SSHRC isn't actually an increase over the standard package. But since our standard funding includes a certain amount of TAing, getting a SSHRC means either not having to spend time grading or running tutorials, or that I can choose to TA for extra money. I'm not struggling at the moment (my partner works a 9-5 job, though we share expenses evenly), but it would be nice to have a bit more of a cushion.
The third is just that my department basically requires us to apply for SSHRC and other external awards as a condition of continuing to receive the standard internal package, so we actually have little choice about whether we want to or not. It's another hoop to jump through.