An average price for .22LR HVHP is 6-7¢ a shot. That's good for small game to about 100 yards.
Average price for 17WMR is 30¢ a shot. It's good to about 150 yards.
To put it into perspective, not counting brass, I can reload my .22 Hornet for less. You can also get 5.56mm for not much more.
Although both rimfires have been used for coyotes, neither of them are really suitable for that.
I know that the magnum rimfires have a lot of fans, but I'm not one of them. For me, they're a cure without a disease, offering neither improved performance over other alternatives nor low cost. Personal choice, I guess.