Here is my take on it.
The Sage is smoking something again.
Yes, he is not here to defend himself, but that's ok. I'm sure some people will defend him anyway. His rulings for the last few years have been all over the target. It's like watching a blind archer shoot.
Ok, now you are a large creature.
How much do you weigh?
Why is your Speed still 30? Didn't your stride increase?
How about your armor? You can no longer wear your old stuff. Maybe I can interest you in this large Full Plate that weighs 100 pounds. Oh. 100 pounds along with all of your other new larger equipment puts you beyond your carrying capacity?
Too bad!
If they would have just came up with some good enlargement rules for Enlarge, Polymorph, Righteous Might, etc., we would not be having this discussion.
Instead, the Sage does the "balance belly flop" where he flip flops between his answers based on his game balance decision of the day. Yawn.
Regardless of what the Sage says, here is the most reasonable answer according to the rules:
MM page 12
"Creatures may become larger as they gain Hit Dice. A size increase affects the creature's ability scores, AC, attack bonuses, and damage ratings as indicated on the following tables."
Last I heard, most PCs and most Dragon Disciples are creatures.
MM page 79
"Dwarf: Hit Dice 1d8+1"
So, Dwarves and Halfings and Elves have hit dice. Presumably, Humans do as well. We just happen to call it levels.
Tome and Blood page 56
"At 5th level, the dragon disciple's size increases one step"
Hence, this creature gains the ability changes listed in the MM for increasing in size.
As for this "you get what is listed in the PrC" garbage, sigh. I would not expect them to list ALL of the advantages and disadvantages of growing in the Dragon Disciple PrC just like I would not expect them to list ALL of the advantages and disadvantages of the claw and bite attacks that they get at second level. This ruling is just plain bad.
They grow claws. They grow teeth. They grow larger. They even grow scales. They are a creature. End of story. They gain the size advantages and disadvantages of growing just like they gain the claw advantages and disadvantages, just like any other creature. You ever walk into an armory and ask for an off the shelf pair of gauntlets when you have claws?
Come on Sage! A little common sense in your rulings here. Sigh.
And btw, I think that they should have added Speed increases for larger creatures. Most real world creatures gain a faster movement rate when they grow up. They are not limited to what they were capable of when they were younger. Granted, I do not think it should be double move due to the increased body mass, but the stride increase should make it maybe 50% more for each doubling of size. YMMV on this.