I hate it when I want to buy something online and it turns out they don't allow me to get it delivered by post, but insist on using some poxy courier.

The great thing with the GPO is that if you aren't in when they call, and it won't fit throughthe letterbox, they stick a note through the door, and you can pick it up the package locally at your convenience.

I'd pay extra for that option, if need be. A couple of days delay every few years because there is a strike is a minor inconveniance compared to the nuisance of having to disrupt your days to fit in with an arbitrary delivery date and time.
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As for online banking, I'd never trust it. Banks these days are quite capable of screwing things up even without that extra way of doing it.
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Postal workers don't vote to strike for fun - they've been pushed in a corner by incompetant management, and feel they haven't any option. I very much hope they win, because they are fighting to defend servics that I value a greta deal.