Technically correct. You would buy time well past the end of the universe. Advances in either quantum or conventional computers would not change this. There are theoretical limits at play.

Now, maybe you can find a way to substantially reduce the difficulty of breaking it over brute force. Cryptographers have been trying to break AES for 30 years now and haven't found one that does more than marginal improvement. But it's possible.

How big are your packets at that point? Seems like you're steadily clogging up your web traffic and setting yourself up for disruption vulnerability down the line if your only response is to inflate the size of every message.

It's not enough to simply have your data be secure. You need it to be reliable. And larger packets require more bandwidth which means more robust hardware and more reliable transmission equipment. Also cuts into the viability of stealthy communications if you know the minimum transmission size of your adversary.