Well now there is: The Adam's Runner push bike. This bike sits extremely low to the ground (lower than almost any trike actually, though you can raise the seatpost much higher than what's pictured here) in part because it doesn't require pedals - simply push with your feet to get moving. This allows even the smallest kids who are ready to move on from their trikes with the opportunity to practice their balance and get the feel for a 'regular' bike before they're big enough for a conventional pedal bike. What's more, they can go much faster. Okay, maybe that makes you a bit nervous, but we guarantee it's a plus from the kids' perspective.
There's virtually nothing to maintain on this bike, so it should last through all of your offspring, and at $85 each it's pretty cheap (and healthy) entertainment. For the self-conscious male toddler the bike also comes in blue, and we've got both colours in stock.