And then a million fraudulent microtransactions will add up. Of course, that would never happen in practice, because the Blockchain cannot handle a million transactions in any reasonable time frame.
If the attacker sends the legit transaction and double-spending one at the same time, it will be detected due to the few seconds wait by the payment processor.
and in fact it is quite common to accept "double-spending" since that is really the only way to increase fees to push through a "stuck" transaction. Otherwise you have to wait an indeterminate (potentially forever) period of time until it exits the mempool of all network participants
[1] https://bitcoin.stackexchange.com/questions/81624/can-two-or...
This page (https://github.com/ethereum/wiki/wiki/Design-Rationale) contains a good overview of the UTXO vs Account model with each's strengths and weaknesses.
Yes, there is a risk of double-spending, but since this is a small amount, the cost of the attack may be higher than the benefit. The payment processor can also deploy more full nodes in different geographic locations to monitor and detect potential double-spending transactions in the transaction memory pool.