Networking in a 2 player web game using a player as the server

I'm sure some answers to this are out there, but I had a hard time finding a solid answer to this question from searches. I'm a total newbie when it comes to networking games and networking in general.

I've been playing around with networking in unity, and have what I think is the start of a smooth, fun networked web game. While looking for help and resources for doing some of the scripting, I was surprised how hard it was to find other examples that use the networking setup that I have. It seems like player hosted games generally have a player running a server separately from the actual game client. I on the other hand, have playerA make a game, playerB joins, then they start playing. Once the game starts, both players will send some variables to the other player to keep things synched up nicely, but no disinction is made between the host user and the user who joined.

What are the problems with this setup?

My guesses would be:

• It is prone to cheating and hacking

• It doesn't allow for long term games like Minecraft, where players can edit the world 24/7

Neither of which I'm really worried about. Is there something more detrimental caused by the style of networking I used?