Decentralization is the most important property of Bitcoin

Decentralization is the extent to which many entities are participating in operating the Bitcoin system, and the extent to which power is dispersed between those entities. Decentralization is desired because it makes Bitcoin more likely to have the following properties (see here for the inspiration):


 * The network must always honor the conditions of the scripts associated with unspent outputs. This means that if a user owns Bitcoins, they can't be spent by someone else.


 * No user's fraction of total Bitcoins should be diluted (in excess of the known inflation schedule).


 * When they decide to spend their coins, they will be able to do so without requiring permission from a third party.

The more decentralized Bitcoin is, the less likely it is that some group of entities will interfere with a user's transaction or to pass off invalid transactions as valid. For instance imagine that Alice wants to send some bitcoins to Bob. If one group controlled all of Bitcoin's hashing power they could require any sort of criteria they wanted before they confirmed Alice's transaction. They could require that she identify herself, that she pay an extremely high fee, or that she prove that she paid the appropriate taxes on the money she's sending. If this group also ran all of the full nodes, they could process transactions that were invalid (in effect, changing the protocol) and transfer money between users arbitrarily or create unlimited coins to give to themselves.

Conversely if one million entities each had one millionth of the total hash power, and each ran a full node, then although it would be theoretically possible for them to coordinate to prevent Alice from paying Bob, it would be much more difficult and less likely. They'd have trouble coordinating, and it's unlikely that so many entities' interests align against Bob or Alice that they'd be motivated to tackle this difficult coordination problem. Likely the vast majority of them don't care about this transaction at all, aside from the fees that it pays them. Similarly in a world of one million equally powerful entities, it is far more unlikely that they'll all (or almost all) conspire to spend other people's coins or create Bitcoins out of nowhere. As long as there are some honest nodes, they can sound the alarm to users that other participants are attempting to pass invalid transactions off as valid.

Decentralization is a continuum. If every adult on earth was solo mining with roughly equivalent hardware and running a full node which they personally used to verify transactions, Bitcoin would be much more decentralized than it is today.

Note that decentralization being the most important property of Bitcoin does not mean that we should always do whatever we can to increase decentralization no matter the costs. Decentralization is not infinitely valuable. The thing to consider when evaluating a change to decentralization is: how much more likely does this change make it for transactions to be interfered with? If that likelihood changes only an extremely small amount, then it may be worth making the change if it brings other benefits to Bitcoin.