It’s the other way around: a gateway cannot listen to any of its frequencies and spreading factors when transmitting a downlink on just one. And beware that nodes don’t know when a gateway is not listening, so might very well send at that same time. And then they will send even more messages when they don’t receive the acknowledgement, increasing the chances for collisions with messages from other nodes or gateways, just worsening the problem.
The acknowledgements of confirmed uplinks have a bad impact on your network.
Yes, there is: a gateway has to comply with the same regulations as other LoRaWAN devices (the nodes). So, in regions where a maximum duty cycle is applicable, a gateway needs to adhere to that too. And it needs to handle many nodes within that maximum duty cycle; when handling 1,000 nodes then its duty cycle will be exhausted 1,000 times sooner than that of one of those nodes. And it might also need downlinks for OTAA Join Accepts and ADR.
Excessive downlinks (including acknowledgements for confirmed uplinks) are bad for the network. There’s a very good reason why TTN limits that to at most 10 per node per day.