As an example, assume a block has 10 transactions with a total value of 1BTC. Does a miner get 25 BTC for validating and committing that 1BTC? What's the economics of this model?
Yes, every block gets 25 BTC (at least until sometime next year). The big thing to remember is that each block gets generated about every 10 minutes. The supply of bitcoins being generated is finite (less than 21 million total).
The BTC amount in the transactions in a given block doesn't matter to the overall economics since the amount generated over the lifetime is 21 million no matter what.
Yes, the miner gets 25BTC regardless of the value of the bitcoins in the block. And yes, if blocks were all that small the economics would not make sense at all, but they are not that small, they are almost always much larger. Still, 25BTC per block works out at around $10 per transaction processed at the moment. Which is still an interesting number and is presently funded by the continuing investment flowing into the Bitcoin economy.
The purpose of mining is not just to validate blocks and receive some fees. It's actually a decentralized way of buying bitcoins without any exchange or third party. Free of regulation and censorship. All you have to do is prove that you did some work. So you end up paying in electricity.
That's also why it's called mining.
So if you want Bitcoins, either you do the work or you pay someone else to do the work for you. Notice that's how Bitcoins become worth something in USD or EUR.
One of the core issues with a decentralized payment network is the initial distribution of funds. The Bitcoin protocol solves this by incentivizing participation through paying for its own upkeep in form of new money. The block reward therefore is mainly the initial distribution mechanism.
In fact it is paid out regardless of the number of transactions that are confirmed in a block. Even an "empty block" only reaping the block reward is valid.
On the other hand, the incentives to include and confirm transactions in blocks are two-fold:
Primarily, transactions include a fee which can only be claimed by including the transaction in a block. These fees increase the revenue of the miner for hardly any effort, thus most miners try to include as many as possible.
Secondarily, miners have spent large sums to obtain mining hardware. They are therefore invested in the success of Bitcoin. As you know, Bitcoin is only backed by its utility. Only if users chose Bitcoin over other payment networks miners stand to profit from their investment. It is thusly in the best interest of miners to maximize Bitcoin's utility. A cheap any easy way is to confirm as many transactions.
In conclusion, we can see that the transaction volume does not directly tie into the block reward. However, the overall incentive structure of Bitcoin makes interests of users and miners align fairly well.
Regarding the block reward only as the cost per processed transactions falls short of its full significance.