We could talk about covenant theology, infant baptism, paedofaith, children addressed in Scripture, etc. Those things are all important to me. However, if we were really trying to drill down on my motivation it would be to give my kids a steady diet of home.
Gina and I grew up in liturgical churches. The word was not preached with particular clarity in those contexts, but by the time we were in grade school we knew the Apostles Creed, the Gloria Patri, various forms of confession / absolution, hymns, and benedictions. Despite walking away from these forms in search of better preaching during different phases of life, we could never shake the feeling of being "home" in a more liturgical service (albeit combined with good preaching as well!).
Kids may or may not "get" what an adult "gets" from being in worship. It depends on so much that it escapes generalization. But look at what they do get in addition to exposure to content-filled worship forms - they see their mother, father, friends, and family singing hymns of faith, closing their eyes in confession, offering prayers of intercession, communing at the Lord's Table, opening their Bibles, giving tithes, and joyfully receiving benedictions. Talk about priceless.
My conviction and hope is that my children not only profit from worship now, but perhaps even more in years to come. If the day comes when they are tempted to stray or have strayed - my hope is that the smell of grilled cheese will bring them back home. And if they never leave home they can continue to enjoy a good home-cooked meal.
Should you keep your kids in worship? You betcha.
Train up a child in the way he should go and when he is older he shall not depart from it.