Either move the hold on statement after the first call to plot3(), or issue a
view(3)
command after plotting.
Creating a pile of named variables only leads to problems. Imagine if you wanted to do this with 100 points. With the following example, the code doesn't have to be scaled with the number of points. All you need to do is generate a new colormap of the appropriate length.
% just the points
x = [0 0 0 2 2 2 2];
y = [0 0 0 0.6 0.3 0.3 0.3];
z = [0 0 0 0 0 -0.7 -0.7];
plot3(x,y,z,'ok') %plot points on a graph
hold on;
% rearrange into a series of segments
x = repelem(x,1,2);
x = reshape(x(2:end-1),2,[]).';
y = repelem(y,1,2);
y = reshape(y(2:end-1),2,[]).';
z = repelem(z,1,2);
z = reshape(z(2:end-1),2,[]).';
plot3(x,y,z) %to connect dots and lines
% apply whatever colormap you want to the series of line segments
cmap = hsv(6);
cmap = cmap([1 3 5 4 6 2],:); % to get the same order you used
set(gca,'colororder',cmap)
grid
max_L = 3;
axis([-max_L max_L -max_L max_L -max_L max_L]);
