Overhead
It will create a new connection each time, so it will send the HTTP headers... including the cookie header that may be large.
Also, just "check if there is something new" is another connection for nothing. Connections implies the work of many items like firewalls, load balancers, web servers ... etc.. Probably, establish the connection is most time consuming thing as soon your IT infrastructure have several inspectors.
If you are using HTTPS, you are doing again and again the most expensive operation, the TLS handshake. TLS performance is good once the connection is established and the symmetric encryption is working, but the process of establishing the connection, key exchange and all that jazz is not fast.
Also, when connections are done, log entries are written somewhere, counters are incremented somewhere, memory is consumed, objects are created... etc... etc.. For example, the reason why we have different logging configurations when in production and in development, is because writing log entries also affect performance.
Presence
When is a long polling user connected or disconnected? If you check for this at a given moment of time... what would be the reliable amount of time you should wait to double check, to ensure it is disconnected or connected?
This may be totally irrelevant if your application just broadcast stuff, but it may be very relevant if your application is a game.
Not persistent
This is the big deal.
Since a new connection is created each time, if you have load balanced servers, in a round robbin scenario you cannot know in which server the next connection is going to fall.
When a user's server is known, like when using a WebSocket, you can push the events to that server straight away, and the server will relay them to the connection. If the user disconnects, the server can notify straight away that the user is not connected anymore, and when connect again can subscribe again.
If the server where the user is connected at the moment that an event for him is generated is unknown, you have to wait for the user to connect so then you can say "hey, user 123 is here, give me all the news since this timestamp", what make it a little bit more cumbersome. Long polling is not really push technology, but request-response, so if you plan for a EDA architecture, at some point you are going to have some level of impedance you have to address, like for example, you need a event aggregator that can give you all the events from a given timestamp (the last time that user connected to ask for news).
SignalR (I guess it is the equivalent in .NET to socket.io) for example, has a message bus named backplane, that relay all the messages to all the servers, as key for scaling out. Therefore, when a user connect to other server, "his" pending events are there "as well"(!) It is a "not too bad approach", but as you can guess, affects the throughput:
Limitations
Using a backplane, the maximum message throughput is lower than it is
when clients talk directly to a single server node. That's because the
backplane forwards every message to every node, so the backplane can
become a bottleneck. Whether this limitation is a problem depends on
the application. For example, here are some typical SignalR scenarios:
Server broadcast (e.g., stock ticker): Backplanes work well for this
scenario, because the server controls the rate at which messages are
sent.
Client-to-client (e.g., chat): In this scenario, the backplane might
be a bottleneck if the number of messages scales with the number of
clients; that is, if the rate of messages grows proportionally as more
clients join.
High-frequency realtime (e.g., real-time games): A backplane is not
recommended for this scenario.
For some projects, this may be a showstopper.
Some applications just broadcast general data, but others have a connection semantics, like for example a multiplayer game, and it is important to send the right events to the right connections.
IMHO
Long polling is a good solution for small projects, but became a big burden for high scalable apps that need high frecuency and/or very segmented event sending.