Specialized technical people often look down on supposed fullstack engineers because specialized technical people value mastery over familiarity -- something a lot of FS engineers really try to be exaggeratingly proud of. While familiarity with your stack is great for cross-cutting concerns, mastery is what truly builds great software, not to mention in a timely manner.
Managers are excited about FS engineers simply because if they scoop up good ones, those who really know what they're doing -- masters of several areas of their stack -- they can rotate them effectively at a fraction of a cost, if not for free.
Managers are excited about FS engineers simply because if they scoop up good ones, those who really know what they're doing -- masters of several areas of their stack -- they can rotate them effectively at a fraction of a cost, if not for free.