If you do something like advertise a /32 for each container you can very quickly fill up TCAMs on your network hardware (in particular cheap top of rack switches that are pervasive in data centers).
The entire v4 internet is something like 600k prefixes right now and the routers that can handle that many prefixes at line rate are irritatingly expensive. ToRs as of a couple of years ago when I last tested this would fall over at 1-10k prefixes.
So be careful when looking at BGP solutions because it's very easy to have a BGP topology that doesn't scale, despite it being the exchange protocol for the Internet.