The first sentence is actually a much better jumping off point for the other side of the argument than yours, because the mistakes involved in the statement should set off alarm bells for people who've walked with mathematics.

What do you mean by "place"? What do you mean by "more"?

Are there more places as marked by real numbers between 0 and 1, or places as marked by integers? Could a machine that can count integers 1000000 times faster than people "visit" all those real places between 0 and 1? What would it mean to visit all the places between 0 and 1? Once the machine visited all of them how would it help people explore that territory?

What do the general ratios and rules between paths and areas mean about how much path it takes to cover an area?

The real world is quantized in way that math isn't, of course, but that's one way the analogy can lead you astray.

And even just keeping to the real world rather than math, it's not all about the sheer velocity with which you can cover an arbitrary distance metric. The primary bottleneck is less that velocity than the amount of time you have to direct to place scaled to your capacities. The car's velocity can let you trade some of that time for fast travel between farther places, and with a road network can arguably even increase a certain variety of places, but that's a very different statement than more places. And it's also a wall against attention to everything in between.