Just because you can, doesn’t mean you should.
Say the outage results in a few million messages that need to be retried. Some subset of those few million will never succeed (aka they are “poisoned pills”). At the same time, new messages are arriving.
In your system, how do you maintain QoS for incoming messages as well as allow for the resolution of the few million retries while also preventing the poisoned pills from blocking the queue? How do you implement exponential backoff, which is the standard approach for this?
SQS gives you some simple yet powerful primitives such as the visibility timeout setting to address this scenario in a straightforward manner.
I guess if you're at the point where your engineering time to implement this + all of the features on top of it that you might need from SQS and future maintenance of this custom solution is cheaper than the cost of using SQS, and you have no other outstanding work that your engineering team should be doing instead, this is a viable cost optimization strategy.
But that's a whole lot of ifs, and with customers I've mostly worked with, they're far better served just using SQS.