It does make sense to use distilled water. The complete water profile of the water used to make the extract should still be present in the extract. You should probably be using distilled water with all extract kits for best results. Even if you have decent water you'd still basically be doubling up on the mineral content of the manufacturer's water.
This is it in a nutshell. The maltser in essence already selected the water profile when he mashed the grain and created the wort they concentrated into extract form, so by using only RO water, then you are getting the purest version of what the beer is meant to be.
He may vary well have used tap water in making the extract, but it's HIS tap water, his minerality, his ph.
Think about the famous waters of beers we drink...
Burton on Trent, for British beers for example, Highly minerally.... that's their "tap water" their common water. Or the very soft water of Cologne where the Kolsch is king... Both of those are born from the water around them.
So when brewing beers that derive so much of their essence from those waters, you don't want to cause a conflict with the water you use.
That's why usually when an allgrain brewer is trying to replicate the water, they will use the most neutral water possible, the most mineral free and PH neutral, and that's Distilled/RO water, (Or sometimes you do build some waters from your own tap water if you have gotten a water report and know what's in there,) and you add things to it to match the numbers.
Or they brew ONLY certain beers, which by having a water report and knowing what's in it, that benefit from their water profile. Maybe IPAs have a nice "Punch" with their water, but a stout might possibly taste flat (not in terms of carbonation) and one dimensional, not complex as the grainbill would warrant. So for that they might build water from RO.
So with extract kits it's really the same thing, to get the recipe CLOSEST to what the brewers created you want to use it too.
BUT, will it ruin your beer if you use tap, or mineral water? NOT ONE BIT.... Most new brewers use tap water in their batches... and the beer is fine...
A HUGE amount of Allgrain brewers don't sweat the water issues, and many, like me use tap water (I live in Michigan which except for Flint,) has some of the best water in the country, especially in the Detroit area- we pull our water from the Great Lakes. Our water is fine to drink and if it's fine to drink it's fine to brew with. All I treat (unless I forget) is for chlorine.
I don't play around with water chemistry for 98% of my batches- it's only if I'm trying to replicate a specific beer, like a Burton Pale Ale... then I'll play around from an R.O. base water.
But honestly, I believe that most of the time we won't notice the difference between a tap water beer or a distilled water batch.... for most styles. I brew with a lot of highly ranked Bjcp judges, and most of them can't even distinguish that- only one of my friends can tell when I don't campden my water, but since we're all in Detroit, we are all used to the same water.
Now in terms of extract, will it hurt your beer to use tap water? (and I'm not talking about during boil advisories) NO. But will it matter for MOST of the batches... probably not.. BUT for certain styles using neutral water will put you closest to what the beer was when the brewer created the recipe.... Will it be "Better" than the same recipe with tap water... it would be an interesting experiment with some beer judges to try....
Personally I think it's cool that JP is selling his kits that way. It really goes the extra mile to make the most closest rendition of the beer he wanted you to taste as possible.