Walking Poles for Matera/Pompeii?

Maybe. I'll describe my impressions and hopefully that helps you know if it would be useful.
The issue at Pompeii is the huge cobblestones. I was much younger when I visited and I still remember it was murder on the feet. A pole could potentially help with stability.
In Matera, the sidewalk surfaces are very very slick. I was a bit older, but I recall just a little misting of rain making me feel I really needed to be careful. Be sure your shoes have excellent tread.
Two amazing sites but not where you want to have a spill, so I think being cautious will be prudent!

Pompei doesn’t really have any uphill or downhill but it does have a lot of stepping up and down a foot or so as you walk on the rocks. You can try to follow the accessible route where they’ve put in bridges over all the gaps but inevitably you’ll want to cross the street to get a better view. So a walking stick could definitely help with balance. Good luck!

This is a good example of Pompeii streets: https://cdn.britannica.com/52/159952-050-00D2DCB3/roadway-Pompeii-Italy.jpg

The issue is groups stop and clog the 'sidewalk' areas when its busy so end up stepping up and down into the street more times than you expect looking at the photos. There are strategically placed shorter steps up (Roman design) but expect larger steps up and down when navigating your way around and act accordingly. So there are the large cobblestones, uneven footing and then the constant dodging of other people to get around them.

When you go don't miss the Insula dei Casti Amanti which is an elevated exhibit of archeological dig in action on Via dell’Abbondanza. Also watch the PBS documentary on the new digs before you for added context.

Have a great trip,
=Tod

I don't use a stick much, but make sure that you have a rubber tip option. Much of Pompeii is thoroughly paved with large stones, and you can't always stick a point into soft earth. Another issue in Pompeii is total distance. It's a very large place. Sun and heat are serious matters from May to September, at least. Although there are many Villas to enter, there is otherwise very little shade in Pompeii.

I was going to make Tim's point, Pompeii is all large slippery stones. Not sure there's much for a walking pole to latch onto.

Definitely use the hiking poles with the rubber attachments on the bottom as the rubber will stabilize the hiking poles when you plant them on the stone walkways at Pompeii & Matera. The metal-tipped poles can’t dig into any soil or gravel and so they can slip on the stone surfaces.
And make sure your shoes also have good tread that will help grip the walkways at these great sites.
Happy travels!

In Matera the issue is stairs, lots of them. If you can walk stairs without problems you probably won’t need sticks.
https://images.app.goo.gl/qYAKBVFRDY3GqCPt7