We only get 20s and sometimes 50s from banking transactions, though she is not a collector, and it appears the only way to get tens from a bank are to request them.
Why do customers have to request them at that particular branch? Are they that rare even at banks despite you living in Vancouver, and that city being a heavily populated one? Isn't being forced to request such bills such an inconvenience to customers?
I can see why - the bank you are referring to may be located in a not-so-heavy traffic area. With less customer traffic, there doesn't tend to be very much commercial and customer transactions. And at a branch that involves heavier traffic, the more commercial and customer transactions involved, the quicker it will take to accumulate 1,000 $10 notes deemed unfit for circulation, and the branches with higher volumes of customer traffic can order crisp $10s more frequently than at a less busy branch.
Banks may have policies that they can only order new notes when they accumulate 1,000 or more worn out bills. If the branch doesn't get enough traffic (like say, in a smaller community), they don't order the infrequently used banknotes, as it would be a waste of the branch's money that they could have spent on additional $5s and $20s - both of which have much higher demand.
As I have said before, you'll have a much better chance if you go to a branch in a busy shopping mall that deals with tons of commercial transactions. They'll be most probable to order crisp $10s and all other denominations. Lucky for me, despite the slightly lower volume of traffic, the Scotiabank I deal with in my neighbourhood does order $10s - though they only receive bricks of crisp $10s about 2 or 3 times annually, or if lucky enough, maybe 4 times per year. The branch is fortunate enough to order $10s, and I respect that. I also respect the fact that they get enough commercial and regular customers to be able to order $10s (recycled or crisp).
I'm very grateful that the Scotiabank I deal with even orders $10s. The Scotiabank doesn't even have to order $10s - they can discontinue ordering such bills at any time. And I just bet there are some Scotiabank branches out there that don't even order bills of such denomination.