I hear the same thing is happening with all grocery deliveries (at leat in the UK), Amazon Fresh isn't special in that regard. You probably know current times are rather exceptional.

I'm willing to give Amazon a pass on this one for the moment. I haven't been able to use any grocery delivery services in weeks. If there are time slots available they are getting filled pretty much immediately when they open up, and I've not been lucky enough to catch it.

Do they lack sufficient personnel (deshelvers, drivers) to increase delivery slots?

Essentially. No company can hire enough of those right now.

Increasing pay is the obvious answer. Maybe the profit margin is too thin.