Then I'd say it was to keep parity between small and medium races, otherwise there'd be a fairly big advantage to small drakewardens.It grows to medium-sized at 7th level...which is also when it gains flying speed.
Small characters can ride medium-sized mounts.
"Carrying Capacity. Your carrying capacity is your Strength score multiplied by 15 . This is the weight (in pounds) that you can carry..."
The drake has STR 16, which is 240 pounds carrying capacity. Halflings and gnomes weigh between 37 and 43 pounds. So it's clearly strong enough to carry a small character.
There's no reason a small character couldn't ride this medium-sized creature with flight...except that this ability is badly written. They can literally ride any other medium-sized flying creature that can support their weight from 1st level...but not their personal drake mount...until 15th.
But! Super easy thing to house rule for groups that don't find flight to be an issue. I've had a flying character in low level games (they were melee though), and PHB small rangers could fly on pterodactyls, so ...
Wizards can be selective about things they worry about.