Well, they can with some slight tricks

I currently have a special module like this that handles the subscription and acts as a special dispatcher.
This does not rely on the parent LiveView and the subscription will be cleaned up when the parent LiveView process dies as normal PubSub subscriptions 
defmodule MyLiveComponent.PubSub do
@moduledoc false
def subscribe(%Phoenix.LiveView.Socket{assigns: %{myself: myself} = socket, pubsub, topic) do
if Phoenix.LiveView.connected?(socket) do
Phoenix.PubSub.subscribe(pubsub, topic, metadata: %{pid: self(), cid: myself})
socket
else
socket
end
end
def subscribe(%Phoenix.LiveView.Socket{} = socket, pubsub, topic) do
Phoenix.PubSub.subscribe(pubsub, topic)
socket
end
def unsubscribe(pubsub, topic) do
Phoenix.PubSub.unsubscribe(pubsub, topic)
end
def broadcast(pubsub, topic, message) do
Phoenix.PubSub.broadcast(
pubsub,
topic,
message,
__MODULE__
)
end
def broadcast_from(pubsub, pid, topic, message) do
Phoenix.PubSub.broadcast_from(
pubsub,
pid,
topic,
message,
__MODULE__
)
end
def local_broadcast(pubsub, topic, message) do
Phoenix.PubSub.local_broadcast(
pubsub,
topic,
message,
__MODULE__
)
end
def dispatch(entries, _dispatch_identificator, message) do
entries
|> Enum.each(fn
{_pid, %{cid: cid, pid: pid}} ->
Phoenix.LiveView.send_update(pid, cid, source: :pubsub, message: message)
{pid, _} ->
send(pid, message)
end)
:ok
end
end
And a live component can be something like this:
defmodule MyComponent do
use MyWeb, :live_component
import MyWeb.CoreComponents
@impl true
def render(assigns) do
~H"""
<%= @message %>
<.button phx-event="send">Send</.button>
"""
end
@impl true
def update(%{source: :pubsub, message: message}, socket) do
socket
|> assign(:message, message)
end
@impl true
def mount(socket) do
updated_socket = socket
|> assign(:message, "No message")
|> MyLiveComponent.PubSub.subscribe(MyPubSub, "topic")
{:ok, updated_socket}
end
@impl true
def handle_event("send", _params, socket) do
MyLiveComponent.PubSub.broadcast(MyPubSub, "topic", "We got a message!")
{noreply, socket}
end