One issue I've seen is that a person who devotes 100% of their time to integration can lose their quantitative engineering skill -- it's a "use it or lose it" phenomenon. The folks who manage to cling to that work end up becoming the only ones who can do it, resulting in a sort of caste system with no relation to actual productivity.

However, in my experience, the best integrators are worth their weight in gold. It requires a mental organization, patience, and discipline that I don't possess. The ones who do it badly are the ones who are racking up dependencies and technical debt.