"Integration into your products" is too narrow. For example, AGPL may mean that contractors who use company internal web services must be given access to the source code of those services. That's a frightening prospect for companies.
And even if not, developers might use internal code search, find what they want, and then copy and paste. The pushback on AGPL code (and GPL code even) comes from the difficulty of establishing internal policies to keep the code segregated. Much easier to have simple-to-undersatnd policies enforced at the boundaries, e.g. "no AGPL, period", instead of "AGPL code is OK for software that won't interface with our systems, as determined by either biased engineers or technically-shaky lawyers."