Right, OP seems to be confusing the BTC value of unspent outputs with the count of unspent outputs.

OP: UTXO db is there to keep track of spendable outputs, irrespective of their combined value.  I think your intuition is correct that the value of UTXO should be increasing over time because of the block reward (it is possible to "burn" bitcoins by sending them to unusable addresses, but I think you're right about the trend).

However, you have to consider the way transactions actually work (in the simple case): they assign a number of Satoshis to a script which specifies spending conditions.  In the case of sending N Satoshi's to address A, what you're doing is creating a script which says that a good signature from the private key corresponding to address A is good enough to spend N Satoshi's.  These N Satoshis are then in an unspent output waiting for someone with the private key for address A to send them elsewhere.  Now, imagine this, someone else sends M Satoshis to address A in the same fashion, there are now N+M spendable satoshis for the person with the private key for address A, but there are two outputs in the UTXO db that represent them (the two transactions which funded address A).  If the person with address A now sends those M+N satoshis to address B, We just got one less unspent output in the UTXO.  The value M+N is still there, but it's now stored in a single unspent output instead of two.

You can find out more about this stuff by looking at raw transactions and how they work.  You'll see that when your wallet sends a transaction to spend X, that transaction might have any number of inputs and may have more than one output as well (change addresses, etc).

Have fun!