I noticed that with Lidoderm patch the pain of tingling and prickling are helped quite a bit even after patch is removed for the day.

How many Lidoderms did you use per day?

I've never used more than one patch a day.

I used them mostly for my meralgia paresthetica in my right thigh, several years ago.

For my feet, I cut one in half and use on both insteps for terrible
times, which are few this past year. I've also used 1/2 behind my knee, for several days at a time...that is my bad knee.

And a few times on my back, and lower sacral area, when I had that groin pull that was so painful.

So I've been quite conservative with them. I do think they stop the nerves from firing eventually perhaps in some cases.
The MP needed daily patch for 2 weeks (it was a very severe pain thing of years longstanding), and now I don't need it anymore! The feet 2 or 3 days, per flare, and the knee up to 5 days in a row. I think based on my experience nerves may stop firing and the pain goes way down.
Then you don't need the patch anymore until a flare again.

When I first started them, for the MP... I had some palpitations and fast heart rate... and that sort of scared me into being cautious with them. But over time I don't see others complain about it and it is not showing up much in the studies etc.
It might have been "just me".

I think they are very valuable, for sharp identifiable nerve pain.
I've never used them for general burning. I use the Biofreeze for that, because it can go up my lower leg about 1/2 up to the knee.
I don't know which nerves are supplying that more global symptom so I haven't used the patches for that type.