I saw that mentioned on Apple Insider a week or so ago. Not a bad idea. Of course, the resulting device is much much larger, since it contains two AA-size batteries.
I’d also be concerned that alkaline batteries tend to leak when they are fully drained or get old. Leakage may damage the Air Tag. So I’d recommend using Lithium metal batteries, which generally do not leak. But doing so may subject the device to air travel restrictions, undermining one of the key use-cases for AirTags.