that way we can find our target very fast, right?
No. Because finite fields are, well, finite. If your key is 1234, then if you use 50 as your step, you will reach 1200, and then 1250, so you will jump over that, without noticing, that you missed it. And then, you will go up from 1250 to that huge n-value, and pass it a few times, to finally land on 1184, and then on 1234.
If you want to better understand that, maybe start with some smaller numbers first? This is a good starting point: "p=79, n=67, base=(1,18)". And when those numbers will be too easy for you, then you can go into higher, and higher values, climbing into bigger curves, by walking one step higher at a time.
For example, target 1000, divide by 2 = 500, if we keep adding 10 to 500 we would reach 1000 after 50 steps and in 51st step we would see 1010,
This is still small enough to make an image out of that. For example, vjudeu made a repository, where you can find all curves from 1 to 1000:
https://github.com/vjudeu/curves1000/tree/master/pngWhich means, if you have for example p-value around 1000, then you can just draw some 1000x1000 image, and put a white dot on (x,y) coordinates. In this way, you can see all points on some small curve, and explore exactly, how coordinates change, when you change your private keys.
Also, in this way, you can easily see, why prime numbers are used. If you have "p=967, n=907, base=(1,88)", then this is acceptable, and if you look at this image, there is no obvious weakness:
https://raw.githubusercontent.com/vjudeu/curves1000/master/png/967.pngHowever, if you pick some complex numbers, then you can notice, how weak some of those curves are. For example, if you take 999:
https://raw.githubusercontent.com/vjudeu/curves1000/master/png/999.png