Why would someone else recognize that I mined some bitcoins? There is zero incentive in itself to do that as you explain it. Why should I not go out and modify my client with the end result being that nobody recognizes any bitcoin anymore and you have a broken system?
There are two pieces to recognizing a block that is generated: fellow miners and "non-miners" on the network.
The selfish incentive to somebody who generates a block is that they want to be a part of the "longest chain" (in terms of demonstrated CPU effort), and as a result they want to grab as many blocks made by others and tack their own block onto the end of that chain. If "their block" is on the longest chain, all other chains or blocks will be ignored by the design of the network. Nodes which aren't miners will ignore those block chains which don't have that proof of work. Therefore under "normal circumstances" it really is to the advantage of a miner to recognize any block which is generated... provided it follows the current proof of work standards so it won't get rejected. Other miners will in turn want to build upon that longest chain as well at the expense of shorting chains.
The "non-miners" will recognize a block you make because you have included their transactions into that block, including future transactions they may be involved with if they are receiving Bitcoins. Therefore it is in the self-interest of a non-miner to propagate at least the blocks their transactions are coupled with, and on a more general note also other transactions as well if they ever expect to receive some of those bitcoins from others.