Blackbeard said it himself that pirates are just those with common interests and that none of his crew sailing with him are ‘friends.’
When common interests are no longer found betrayal will happen(and Kaido’s words will be true because he said pirates betray each other). If I recall Blackbeard doesn’t trust Shiryu and with right suspicion since he legit murdered a bunch of people 10s after he got his sword back. This is likely the right attitude to have since Blackbeard that betrays and has killed so many people he likely would be naturally suspicious of others. Pizarro wanted to be captain too(maybe as a joke?), but Laffitte threatened him with death so you know Pizarro’s loyalty is in question possibly.
It’s very likely that outside of Jesus Burgess, Doc Q and Van Augur no one is actually loyal to Blackbeard(if the original 3 are even 100% loyal to Blackbeard themselves at all). The other crewmates like San Juan Wolf, Vasco and Devon are likely only in being in Blackbeard’s Crew for wanton death, the promise of power and destruction because as level 6 prisoners what other things could they follow?
When Blackbeard is at his weakest he will be betrayed and abandoned leading to his demise. If Blackbeard is no longer powerful what is there left of him to follow? This would be in contrast to Luffy’s crew who all 100% are loyal to him and would die for him.