Airline fares, mileage & actual benefits

Spring break is coming up & got me thinking into travel & travel plans..
Is it ever possible to use that so-called mileage we do collect from the various assortment of airlines I have traveled in the last decade & more..
I believe I have the required amount on atleast one-of-those so called "Free " flights.. but have I ever used it ..nope never kaput!
More thinking led to my eureka moment..
Interestingly I have been buying airline fares for my kids for last N number of years. As read by me, kids do not qualify on mileage .. whatever restrictions that they may be. As I see it, infant fares are only for the first 2 years of life. What after .. later its just a measly $100 or so less than what I pay (for international) and none-whatsoever for domestic travel.
So, interestingly, should'nt the mileage benefits be recurred by the parent/ paying party...
I thought mileage is the so called incentive that airlines offer us cattle-class individuals hell-bent on making that journey whether we can afford it or not.
In which case my kids travel miles should be mine all mine.. or rather my poor hard-working husband's. Now that sounds like a good incentive to stick to a particular airline in this Internet-best-price-airline hunt world. And I might actually get to use those bugger miles for some much needed pleasure travel.
I hope some-fast thinking airline CEO actually believes in this idea and helps us poor-debt-ridden parents and award us with some serious vacation benefits.
Interesting thought for me while picking the kids up at valet today !