Is it a problem that miners participate in a pools?
It can be. The most widely-used mining protocol at present (and the historically popular protocols) give complete control over what gets mined to the pool operator. Even if the pool operator has the best of intentions, they can be hacked and their hash rate abused for evil. This is what allegedly happened when the mining pool GHash.io (with about 30% of hash rate) stole about $100,000 in BTC from the betting website BetCoin Dice.
But it doesn't have to be a problem. One current mining protocol, GetBlockTemplate, theoretically allows pools to give individual miners the ability to select which transactions they include in their blocks, preventing the pool from centrally making important decisions. Another system, Peer-to-Pool Pool (P2Pool), is a completely decentralized pool where there is no pool operator, just a bunch of independent miners collaborating without any one of them making decisions for the others.
Both of these protocols have problems. GetBlockTemplate (GBT) is bandwidth intensive, complicated, and not very flexible; P2Pool is complicated, less efficient than centralized pooling (it can't include as many fee-paying transactions in a block), and doesn't necessarily work well for very small miners.
A new alternative to both of these protocols is BetterHash which looks like it many work much like GBT was supposed to without the problems.
I think there are some possible ways to prevent miners from pooling. For example add miner signature to the block header, so pool will not be able to disclosure their private key to outsource calculations.
This solution has been proposed many times before and it certainly could be added to the Bitcoin Protocol. However, several experts worry that it would make centralization worse by only providing the benefits of pooling to the biggest individual miners. Smaller miners who now couldn't join pools would be subject to increased block-finding variance and so would either be more likely to go out of business, or would simply rent hash rate from a large miner who would operate the equipment and payout rewards---increasing centralization in either case.