Why doesn’t BTC reward miners for confirmations, too?

Currently as far as I know when a miner discovers enough 0s, he
broadcasts his solution to the network in order to win the coins.

While, he broadcasts his solution (which gave him the 0s), he also
verifies some transactions.

When miner verifies transactions, the gives priority to the transaction
that pays the highest confirmation fee.

As far as I understand, when the miner verifies transactions that do not
pay any confirmation fees, the miner doesn’t get any rewards for doing so.
In such a case, the miner has absolutely no reason to care to verify it.
If the miner verifies such a fee-less transaction, he does it purely
because he is just a kind person, but no monetary incentives for this act.

My question is: why doesn’t the BTC protocol define the BTC reward
function as a function of the solves 0s and as a function of number of
confirmations?

Specifically, I propose this reward function:

btc_reward = ZEROS_DISCOVER_REWARD
for transaction in confirmations:
    already_has_n_confirms = get_confirms_num(transaction)
    confirm_reward_rate += L / (1 + E**(K*already_has_n_confirms)
    btc_reward += confirm_reward_rate * CONFIRM_REWARD

where L, E, K and CONFIRM_REWARD are variables that need to be
tuned to adjust BTC’s inflation/deflation targets (similar to like how
ZEROS_DISCOVER_REWARD is defined).

Of course this is just a suggestion for funrction with an exponential decay
as a function of number of confirmations a transaction already has. E.g.
transactions with no confirmations are in a more disperate situation to get
some confirmation that other transactions that have, say, 10 confirmation
salready.

This way, miners will have a monetary incentive to confirm all transactions
even those that pay no confirmation fees, which will effectively reduce
the resistance against trade in the BTC world, and make BTC even more
attractive.

At the same time, people who are in a hurry can still put
their fees to get their confirmations faster. But at least, those who are
engaging in a low-cost economy that is sensitive to fees at least have the
liberty of having a free monetary system.

Any thoughts on why this isn’t done?