I would say there are the same privacy issues as BitTorrent, IF you are using it publicly or for a service that is known to be criminal or “unapproved of.” Basically IP addresses are exposed like any normal clearnet if someone at scale is trying to ping and investigate what every peer is doing. 

The reason it’s hard to call this a “trade off” exactly however is because this is literally no different than it’s ever been, to the contrary it’s better in a P2P system like this than with normal internet usage. You have more privacy because there’s not any indication as to what is being communicated, what you are connecting to, or why. (Everything is a generic key, not a visible, discoverable domain like ReallyWeirdFetish.com or something)

So it’s more of an “it doesn’t really solve privacy” consideration rather than a trade off.

Another case could be made for DDOS risk, since you are working directly with your personal IP address. You’re a bit more open to attack in P2P than through using central servers and services to connect through. But that’s really kind of a dodge, a little like saying “well if you hold your keys you might lose your bitcoin.” Yeah sure, but that just comes with being sovereign.

Lastly is that P2P is often less reliable for data persistence, but this is a device problem, not a P2P problem. If you treat a peer node like a server, it’ll be as reliable as a server.

Honestly from everything I’ve dug into, from a purely theoretical sense, there just aren’t that many trade offs, aside from calling the fact that it doesn’t solve every single problem that we may want a “trade off.” But in regards to the alternatives… it’s just better.