It's worth some concern.
As the copay attack shows, that everyone uses these libraries doesn't let us rest assured. There are virtually zero eyeballs on the code of transitive dependencies because you would have to extract tarballs to read code. And attacks can be extremely targeted. The copay attack was only discovered because of a deprecation warning in the attacker's code that someone reported.
https://hackernoon.com/im-harvesting-credit-card-numbers-and...
His section about circumventing CSPs was particularly interesting and relevant. CSPs were an impediment to him, and he avoided operating his scam on sites where a CSP was installed.
It really isn't normal to have 1000+ dependencies and it really isn't safe. Just saying "CSP will protect us" isn't good enough.
I do. That is why I don't have many deps in general. Transitive or not. With only a handful of dependencies that are from trusted sources and that are audited by me I can be sure that they are safe.
With 1000+ dependencies that are from as many random sources you can not do the same.
Having 10 dependencies is drastically different from a security aspect then 1000+.