You can accept an answer to any of your questions, noting the answer that helped you the most. You can then go back after getting 15 rep and vote on the others that you thought were useful.
I tend to agree that this is a little .. well, suboptimal, because it depends on humans remembering to go back and do things after an undetermined amount of time has passed. 15 rep isn't that hard to get once you learn the ropes, but I do appreciate your frustration.
We're considering the idea of saving your votes and then applying them once you get to 15 rep (up votes) or once you get to 125 rep (down votes), but there are some interesting challenges there (such as what would happen if you ran into a deficit since down-votes on answers cost 1 rep).
Totally blue-sky at this point, nothing more is happening beyond us talking about it, but it's something we'd like to make less frustrating. We tell people "Hey, you need to sign in to vote on this post", then they sign in, and they still can't vote - it drives people a little crazy.
The system as it currently is helps prevent gaming the system by growing 'sock puppet' accounts that are used to vote for one another systematically - that's why the restriction is there. We might have come up with a way to allow mostly unlocking the privilege much sooner, with safe guards still in place.