The primary reason that large banks don't invest in startups is that they are risk averse. Startups are by their very nature high risk ventures - most of them fail. That's why VCs are willing to invest in them, because the upside potential is also high. Banks, on the other hand, are in the business of managing other people's money and so they have to be much more careful about where they invest it.
There are also regulatory reasons why banks may be hesitant to invest in startups. Banks are heavily regulated, and there are restrictions on what kinds of investments they can make. Startups may also be engaged in activities that fall outside of the scope of what banks are allowed to do.
So, while it's not impossible for banks to invest in startups, it's much harder for them to do so than it is for VCs.