You are blatantly ignoring the fact that it took Kaladin around 10 months to form a bond song enough with Syl to draw in Stormlight. This is inherent in spren transitioning from the cognitive realm to the physical realm, it takes time for them to regain their memories and form the bond with their radiant. Before this The Lopen had been trying to suck in stormlight everyday if he was forming a bond with a spren it would have been mentioned (not to mention that rock would have noticed his spren because it would have had to start when he first joined up).
So we've established it has to take time because of the inherent nature and not do to the disobedience and since we have no evidence of him having a spren the only alternative is that he is a Squire of which as mentioned in the books wind runners normally have a great number.
There came also sixteen of the order of Windrunners, and with them a considerable number of squires, and finding in that place the Skybreakers dividing the innocent from the guilty, there ensued a great debate.
-From Words of Radiance, chapter 28, page 3
Furthermore the Nahel bond binds a spren to a person by entwining itself in their spiritweb. Since the spiritweb is the spiritual aspect of person the bond itself is of the spiritual realm
A Surgebinder's Nahel bond with a spren may work in a similar way, a spren becoming spiritually attached to a certain point on a person's Spiritweb, sort of like a non-invasive form of Hemalurgy.
-from the coppermind