First of all, Kuzan probably didn't have a bounty before Egghead, the public as a whole didn't know about him being a Blackbeard pirate, not even Jimbei who was in Big Moms crew at that time knew, with Doflamingo only having heard rumors. Only the Gorosei and Sakazuki seem to know. Garp even tells him to get his ass back in uniform, meaning he probably wasnt an official criminal until now.(Though, some people think he may have gotten a bounty during Wano, because he kidnapped Pudding, nothing has been confirmed yet though)
Second, while Teach is at 3.9 billion, he will surpass this bounty soon, he took out Law, who was at 3 billion and his crew kidnapped Garp. There is also his crew fucking around on Egghead but, idk if a crime was committed their exactly, or at least not something public. We also know Laffite is plotting something, and he has a dude who knows about the ancient weapons working for him. So teach will surpass 4 billion pretty soon, Kuzan realistically could achieve this bounty since:
Him leaving the Marines and joining a pirate crew is inherently disgraceful. CP0 wanted Who's fucking who dead for joining the beast pirates, and he was already a criminal and no one knows who he is, meanwhile Kuzan is a world famous marine(public face of the government). with even Warcury pointing out how this is a disgrace to the marines
He knows marine secrets and generally has Intel to give to Blackbeard, which is obviously a threat.
He kidnapped Pudding, someone who can maybe read the RP
He froze Cracker
He kidnapped Garp, and is now attempting to hold him ransom for the government
4b is also, in the middle between the admiral CG bounties, and the Fleet admiral CG bounties
