ASP.NET application integration into a Sharepoint publishing portal

This is not going to a one-time post to explain the A to Z, but it is really my murmur. I find the solution (I hope I could) as I find problems.

It seems to be a concensus that to this i.e. ASP.NET application integration into Sharepoint, web parts is the way to go.
Below is an extract from a blog post.
1. Convert each Asp.Net page into one or more Asp.Net User Controls.
2. Deploy the controls to the ControlTemplates directory.
3. For each page in the Asp.Net app, create a custom page layout containing its respective User Control(s).
4. Deploy the page layouts to the target site, and create a single page instance for each page layout.

But, frankly, I do not understand why. Why we go for the web parts solution.
We can run an arbitrary aspx page (with code behind class) in a Sharepoint site. This seems simpler to me.

From the next post, I will show you here the steps I took.