I know, I perfectly get that, it's obvious that having a straight fork but with an angle at the joint with the head tube will have the same effect. What I was saying is that in the previous posted picture, just that picture, the increased rake of that very specific bicycle was likely consequence on the curvature, so I am not sure how we did get here to be honest.

Hey! Easy tiger...

The rake of the fork is created ONLY by the curve of the blade the blue bike. That said, the rake is pretty normal and not big big factor. The lack of toe overlap is caused more by the long top tube and even more by the 70 degree head tube.

And yet again, we agree. Although assuming that a specific bike size is needed and that a particular bike geometry (like in the case of the parallax) it is what it is sometimes I suppose, I repeat suppose not stating, that increasing the rake, reducing the crank arm length or wheel size are the only three viable options.

What I will be curious to discover now, is why reality is different from the output of bikecad and the basic math you can do, like 540 (front wheel) - 165 (crank arm) - 336 (radius of a 700/23) it leaves 39mm and that assuming no q-factor at all... how is it possible the tyre rubs/touch the crank?

One thing to consider is that a 165mm crank arm is actually a good bit longer than 165mm. Probably closer to 185.

What is the 540 (front wheel) number you are using?

If you measure to the end of the crankarm, yeah. To the center of the pedal spindle it should measure true to size. Wait, why am I doing this?

Still, that would leave you 19mm. As per the 540 is said front wheel but I meant front centre and I took the value from here Mash Parallax - Cinelli for the size XS.

I suppose I'll have to wait when I get the frame in the upcoming weeks and I'll swap components with my current one. If it rubs I'll start looking for a 155mm crank which could be better for me anyway.

Because you can't resist internet calling you

Well it aint the hole that hits the front tire.

Here we are my build is now complete and here is my personal truth about the crank overlap. I got myself a parallax size XS(50) with a sugino 75 dd 165mm and 25mm schwalbe one tubeless tyres. Attached the clearance or lack of depending by how you see it. Toe overlap? Yes, but neither the crank arm nor the pedal touches the tyre