The only downside to more connections is increased bandwidth usage and slightly more CPU usage. Here, it's estimated that 2000 transactions per second is 7.8 megabits/second (average residential connect speed) and Bitcoin operates at the most at 7 TPS currently so you're in the clear.
Why you should connect to more nodes.
The more nodes you are connected to the more up to date you will be on network status and vice-versa. If the network comes up with a new block, you will be one of the first few notified.
If your mining pool comes up with a block, you will want to push your block out to the network as fast and spread as possible. You want as many nodes to know about your new and valid block as possible. Of course a new block incurs a domino effect with nodes, one node that knows of your block will tell other nodes about it. You can reach all nodes faster if you notify many nodes.
Why do I need nodes to know about my block?
Mining is a competition, you are competing against a massive amount of other players who all are probably hashing faster than you. It's very likely that they will also find a block in the time you do, this happens often. But only 1 block can be accept, and block acceptance is based on network majority. If you mine a valid block at the exact same time as another miner, and you can get a good majority of nodes your block, you will get the reward. The other block turns into an orphaned block and the miner who mined it loses all profit.
It's suggested you connect to as many large node as possible, you don't have to necessarily connect to smaller nodes as large nodes will rebroadcast your block to many small nodes. You may see some increased bandwidth usage but it's negligible considering what kind of connections servers tend to have.
Concerning transactions fees
Connecting to more nodes will net you more transactions to put into blocks, but it really won't be much. The 10 minute block time Bitcoin has means your node will have ample time to put together enough transactions for profit.
8 peer connections is not a lot and may mean you aren't receiving any inbound traffic.